## Qian, Tao

Compute Distance To:
 Author ID: qian.tao Published as: Qian, Tao; Qian, T. Homepage: http://www.fst.umac.mo/en/staff/fsttq.html External Links: GND
 Documents Indexed: 219 Publications since 1984, including 1 Book 4 Contributions as Editor Reviewing Activity: 3 Reviews Co-Authors: 109 Co-Authors with 190 Joint Publications 2,933 Co-Co-Authors
all top 5

### Co-Authors

 31 single-authored 21 Dang, Pei 19 Chen, Qiuhui 15 Yang, Yan 14 Deng, Guantie 12 Mai, Weixiong 10 Zhang, Liming 9 Kou, Kit-Ian 9 Tan, Lihui 9 Wang, Jinxun 8 Sommen, Franciscus 7 Mi, Wen 6 Li, Haichou 6 Li, Pengtao 6 Sabadini, Irene 6 Wang, Yanbo 5 Gaudry, Garth Ian 5 Li, Luoqing 5 McIntosh, Alan 5 Yang, Qixiang 4 Chen, Xingdi 4 Colombo, Fabrizio 4 Fei, Minggang 4 Ku, Min 4 Li, Shuang 4 Li, Youfa 4 Zhong, Tongde 3 Alpay, Daniel Aron 3 Baratchart, Laurent 3 Dong, Baohua 3 Du, Zhihua 3 Gao, You 3 Long, Rulin 3 Mo, Yan 3 Mourão, José 3 Nunes, João Pedro Vidal 3 Peng, Lizhong 3 Qu, Wei 2 Cowling, Michael G. 2 Fu, Wenyuan 2 Gong, Yafang 2 Huang, Yun 2 Ji, Xinhua 2 Kwan, Chiman 2 Li, Chun 2 Li, Xingmin 2 Li, Yanting 2 Rodino, Luigi 2 Schulze, Bert-Wolfgang 2 Wang, Jianzhong 2 Wang, Xiaoyin 2 Xu, Roger 2 Xu, Yuesheng 2 Zhang, Yanhui 1 Axelsson, Andreas 1 Pinheiro de Castro, Luís Filipe 1 Chang, Der-Chen E. 1 Chen, Hongda 1 Chen, Jiecheng 1 Chen, Luping 1 Chevillard, Sylvain 1 De Martino, Antonino 1 Delanghe, Richard 1 Du, Jinyuan 1 Fujiwara, Hiroshi 1 Guo, Yuanyuan 1 Hempfling, Thomas 1 Ho, Io-Tong 1 Hong, Wei 1 Huang, Yong 1 Kähler, Uwe 1 Kirwin, William D. 1 Lee, Weijen 1 Leong, Ieng Tak 1 Leong, Iengtak 1 Li, Dengfeng 1 Li, Zhixiong 1 Liu, Dangzheng 1 Liu, Hua 1 Liu, Shuang 1 Lv, Jianhao 1 Lyu, Xiaojing 1 Peetre, Jaak 1 Peña Peña, Dixan 1 Rao, Hangmei 1 Ren, Guangbin 1 Ren, Zhubing 1 Saitoh, Saburou 1 Sheeley, Joseph 1 Sjogren, Peter 1 Sprößig, Wolfgang 1 Stessin, Michael I. 1 Tan, Chunyu 1 Wan, Feng 1 Wang, Rui 1 Wang, Silei 1 Wegert, Elias 1 Wu, Hau-Tieng 1 Wu, Hio Tong 1 Yan, Dunyan 1 Yan, Lixin ...and 9 more Co-Authors
all top 5

### Serials

 21 Mathematical Methods in the Applied Sciences 16 Complex Variables and Elliptic Equations 12 Journal of Mathematical Analysis and Applications 11 International Journal of Wavelets, Multiresolution and Information Processing 10 Complex Analysis and Operator Theory 9 Advances in Applied Clifford Algebras 5 Applied Mathematics and Computation 5 Journal of Functional Analysis 5 The Journal of Fourier Analysis and Applications 5 Acta Mathematica Scientia. Series B. (English Edition) 5 Science China. Mathematics 4 Applicable Analysis 4 Chinese Annals of Mathematics. Series B 3 Journal of Mathematical Physics 3 Arkiv för Matematik 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Automatica 3 Journal of Differential Equations 3 Science in China. Series A 3 IEEE Transactions on Signal Processing 2 Computers & Mathematics with Applications 2 Studia Mathematica 2 Journal of Geometry and Physics 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Proceedings of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 Zeitschrift für Analysis und ihre Anwendungen 2 Complex Variables. Theory and Application 2 Physica D 2 Journal of the Australian Mathematical Society. Series A 2 Scientia Sinica. Series A 2 Applied and Computational Harmonic Analysis 2 Advances in Computational Mathematics 2 Taiwanese Journal of Mathematics 2 Scientia Sinica. Mathematica 2 Trends in Mathematics 1 Journal of the Franklin Institute 1 Acta Mathematica Sinica 1 Canadian Mathematical Bulletin 1 Colloquium Mathematicum 1 IEEE Transactions on Automatic Control 1 Journal of Approximation Theory 1 Journal of Computational and Applied Mathematics 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Monatshefte für Mathematik 1 Results in Mathematics 1 Journal of Operator Theory 1 Systems & Control Letters 1 Advances in Mathematics 1 Approximation Theory and its Applications 1 Revista Matemática Iberoamericana 1 Applied Mathematics Letters 1 Journal of Integral Equations and Applications 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 The Journal of Geometric Analysis 1 Kexue Tongbao 1 Acta Mathematica Sinica. New Series 1 Applied Mathematics. Series B (English Edition) 1 Methods and Applications of Analysis 1 Abstract and Applied Analysis 1 Acta Mathematica Sinica. English Series 1 IEEE Transactions on Image Processing 1 Nonlinear Analysis. Real World Applications 1 Journal of the Australian Mathematical Society 1 Acta Mathematica Scientia. Series A. (Chinese Edition) 1 Communications on Pure and Applied Analysis 1 Chinese Journal of Contemporary Mathematics 1 Computational Methods and Function Theory 1 Boundary Value Problems 1 Journal of Pseudo-Differential Operators and Applications 1 Springer Proceedings in Mathematics & Statistics 1 International Journal of Systems Science. Principles and Applications of Systems and Integration
all top 5

### Fields

 102 Harmonic analysis on Euclidean spaces (42-XX) 99 Functions of a complex variable (30-XX) 37 Information and communication theory, circuits (94-XX) 28 Several complex variables and analytic spaces (32-XX) 24 Functional analysis (46-XX) 23 Approximations and expansions (41-XX) 21 Operator theory (47-XX) 18 Numerical analysis (65-XX) 15 Partial differential equations (35-XX) 14 Potential theory (31-XX) 11 Integral transforms, operational calculus (44-XX) 11 Systems theory; control (93-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 7 Probability theory and stochastic processes (60-XX) 6 Integral equations (45-XX) 5 Statistics (62-XX) 4 General and overarching topics; collections (00-XX) 4 Quantum theory (81-XX) 4 Biology and other natural sciences (92-XX) 3 Abstract harmonic analysis (43-XX) 3 Computer science (68-XX) 2 Number theory (11-XX) 2 Measure and integration (28-XX) 2 Special functions (33-XX) 1 Nonassociative rings and algebras (17-XX) 1 Real functions (26-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Fluid mechanics (76-XX)

### Citations contained in zbMATH Open

159 Publications have been cited 1,373 times in 496 Documents Cited by Year
Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces. Zbl 0817.42008
Li, Chun; McIntosh, Alan; Qian, Tao
1994
Adaptive Fourier series—a variation of greedy algorithm. Zbl 1214.30047
Qian, Tao; Wang, Yan-Bo
2011
Analytic unit quadrature signals with nonlinear phase. Zbl 1070.94504
Qian, Tao; Chen, Qiuhui; Li, Luoqing
2005
Characterization of boundary values of functions in Hardy spaces with applications in signal analysis. Zbl 1086.30035
Qian, Tao
2005
Mono-components for decomposition of signals. Zbl 1104.94005
Qian, Tao
2006
Generalization of Fueter’s result to $$\mathbb{R}^{n+1}$$. Zbl 0909.30036
Qian, Tao
1997
Intrinsic mono-component decomposition of functions: an advance of Fourier theory. Zbl 1188.42001
Qian, Tao
2010
Singular integrals on star-shaped Lipschitz surfaces in the quaternionic space. Zbl 0921.42012
Qian, Tao
1998
Generalizations of Fueter’s theorem. Zbl 1079.30066
Kou, K. I.; Qian, T.; Sommen, F.
2002
Frequency-domain identification: An algorithm based on an adaptive rational orthogonal system. Zbl 1244.93038
Mi, Wen; Qian, Tao
2012
Fourier spectrum characterization of Hardy spaces and applications. Zbl 1169.42003
Qian, Tao; Xu, Yuesheng; Yan, Dunyan; Yan, Lixin; Yu, Bo
2009
Hardy-Sobolev spaces decomposition in signal analysis. Zbl 1211.30061
Dang, Pei; Qian, Tao; You, Zhong
2011
Boundary derivatives of the phases of inner and outer functions and applications. Zbl 1173.31001
Qian, Tao
2009
Algorithm of adaptive Fourier decomposition. Zbl 1393.94142
Qian, Tao; Zhang, Liming; Li, Zhixiong
2011
A fast adaptive model reduction method based on Takenaka-Malmquist systems. Zbl 1256.93029
Mi, Wen; Qian, Tao; Wan, Feng
2012
Fourier analysis on starlike Lipschitz surfaces. Zbl 0991.42009
Qian, Tao
2001
Analytic signals and harmonic measures. Zbl 1082.94006
Qian, Tao
2006
Analytic phase derivatives, all-pass filters and signals of minimum phase. Zbl 1392.94170
Dang, Pei; Qian, Tao
2011
Optimal approximation by Blaschke forms. Zbl 1259.41021
Qian, Tao; Wegert, Elias
2013
Two families of unit analytic signals with nonlinear phase. Zbl 1104.94004
Chen, Qiuhui; Li, Luoqing; Qian, Tao
2006
Stability of frames generated by nonlinear Fourier atoms. Zbl 1086.42018
Chen, Qiuhui; Li, Luoqing; Qian, Tao
2005
Orthonormal bases with nonlinear phases. Zbl 1213.42126
Qian, Tao; Wang, Rui; Xu, Yuesheng; Zhang, Haizhang
2010
A tighter uncertainty principle for linear canonical transform in terms of phase derivative. Zbl 1393.94205
Dang, Pei; Deng, Guan-Tie; Qian, Tao
2013
The Paley-Wiener theorem in $$\mathbb{R}^n$$ with the Clifford analysis setting. Zbl 1015.42013
Kou, Kit-Ian; Qian, Tao
2002
Deriving harmonic functions in higher dimensional spaces. Zbl 1052.30055
Qian, T.; Sommen, F.
2003
An alternative proof of Fueter’s theorem. Zbl 1117.30039
Peña Peña, Dixan; Qian, Tao; Sommen, Frank
2006
A sharper uncertainty principle. Zbl 1284.42019
Dang, Pei; Deng, Guan-Tie; Qian, Tao
2013
Convolution singular integral operators on Lipschitz curves. Zbl 0791.42012
McIntosh, Alan; Qian, Tao
1991
Conformal transformations and Hardy spaces arising in Clifford analysis. Zbl 0856.30037
Qian, Tao; Ryan, John
1996
Adaptive decomposition by weighted inner functions: a generalization of Fourier series. Zbl 1223.42006
Qian, Tao; Tan, Li-Hui; Wang, Yan-Bo
2011
A martingale proof of $$L_ 2$$ boundedness of Clifford-valued singular integrals. Zbl 0814.42009
Gaudry, G. I.; Long, R.; Qian, T.
1993
The $$H^{\infty}$$ functional calculus based on the $$S$$-spectrum for quaternionic operators and for $$n$$-tuples of noncommuting operators. Zbl 1350.47017
Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene
2016
Two integral operators in Clifford analysis. Zbl 1182.30082
Gong, Yafang; Leong, Ieng Tak; Qian, Tao
2009
Singular integrals associated to the Laplacian on the affine group $$ax+b$$. Zbl 0776.43003
Gaudry, G. I.; Qian, T.; Sjögren, P.
1992
Möbius covariance of iterated Dirac operators. Zbl 1043.31500
Peetre, Jaak; Qian, Tao
1994
Cyclic AFD algorithm for the best rational approximation. Zbl 1287.42018
Qian, Tao
2014
Adaptive Fourier decomposition of functions in quaternionic Hardy spaces. Zbl 1254.30086
Qian, Tao; Sprößig, Wolfgang; Wang, Jinxun
2012
Structure of solutions of polynomial Dirac equations in Clifford analysis. Zbl 1054.30049
Gong, Y. F.; Qian, T.; Du, D. Y.
2004
Singular integrals with holomorphic kernels and Fourier multipliers on star-shaped closed Lipschitz curves. Zbl 0924.42012
Qian, Tao
1997
Hardy-Sobolev derivatives of phase and amplitude, and their applications. Zbl 1256.42012
Dang, Pei; Qian, Tao; Yang, Yan
2012
Comparison of adaptive mono-component decompositions. Zbl 1270.94041
Qian, Tao; Li, Hong; Stessin, Michael
2013
Rational orthogonal systems are Schauder bases. Zbl 1306.46023
Qian, Tao; Chen, Qiuhui; Tan, Lihui
2014
Hilbert transforms on the sphere with the Clifford algebra setting. Zbl 1182.30092
Qian, Tao; Yang, Yan
2009
Mono-components vs IMFs in signal decomposition. Zbl 1145.94374
Qian, Tao; Zhang, Liming; Li, Hong
2008
Schwarz lemma in Euclidean spaces. Zbl 1105.30039
Yang, Yan; Qian, Tao
2006
Extending coherent state transforms to Clifford analysis. Zbl 1349.81088
Kirwin, William D.; Mourão, José; Nunes, João P.; Qian, Tao
2016
Cauchy integrals on Lipschitz surfaces in octonionic space. Zbl 1151.30038
Li, Xing Min; Peng, Li Zhong; Qian, Tao
2008
Two-dimensional adaptive Fourier decomposition. Zbl 1347.42047
Qian, Tao
2016
On backward shift algorithm for estimating poles of systems. Zbl 1296.93068
Mi, Wen; Qian, Tao
2014
Tighter uncertainty principles based on quaternion Fourier transform. Zbl 1338.42013
Yang, Yan; Dang, Pei; Qian, Tao
2016
Remarks on adaptive Fourier decomposition. Zbl 1267.42006
Qian, Tao; Wang, Yanbo
2013
Phase derivative of monogenic signals in higher dimensional spaces. Zbl 1275.30027
Yang, Yan; Qian, Tao; Sommen, Frank
2012
$$L^p$$ polyharmonic Dirichlet problems in regular domains. II: The upper half plane. Zbl 1256.31002
Du, Zhihua; Qian, Tao; Wang, Jinxun
2012
Adaptive decomposition of functions into pieces of non-negative instantaneous frequencies. Zbl 1200.94026
Qian, Tao; Ho, I. T.; Leong, I. T.; Wang, Yanbo
2010
The Paley-Wiener theorem in the non-commutative and non-associative octonions. Zbl 1176.42019
Li, XingMin; Peng, LiZhong; Qian, Tao
2009
Rational approximation of functions in Hardy spaces. Zbl 1353.30032
Deng, Guantie; Qian, Tao
2016
Sampling theorem and multi-scale spectrum based on non-linear Fourier atoms. Zbl 1171.94331
Chen, Qiuhui; Qian, Tao
2009
Adaptive orthonormal systems for matrix-valued functions. Zbl 1370.47011
Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene
2017
Hilbert transforms and the Cauchy integral in Euclidean space. Zbl 1168.45001
Axelsson, Andreas; Kou, Kit Ian; Qian, Tao
2009
Fueter mapping theorem in hypercomplex analysis. Zbl 1330.30005
Qian, Tao
2015
Coherent state transforms and the Weyl equation in Clifford analysis. Zbl 1355.81076
Mourão, José; Nunes, João P.; Qian, Tao
2017
Estimation of hyperbolically partial derivatives of $$\rho$$-harmonic quasiconformal mappings and its applications. Zbl 1317.30025
Chen, Xingdi; Qian, Tao
2015
Adaptative decomposition: the case of the Drury-Arveson space. Zbl 06829778
Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene
2017
Aveiro method in reproducing kernel Hilbert spaces under complete dictionary. Zbl 1382.30005
Mai, Weixiong; Qian, Tao
2017
Fourier multipliers on Lipschitz curves. Zbl 0766.42005
McIntosh, Alan; Qian, Tao
1992
Boundedness of singular integral operators with holomorphic kernels on star-shaped closed Lipschitz curves. Zbl 0860.42013
Gaudry, Garth; Qian, Tao; Wang, Silei
1996
Transient time-frequency distribution based on mono-component decompositions. Zbl 1316.94025
Dang, Pei; Qian, Tao; Guo, Yuan Yuan
2013
2D partial unwinding – a novel non-linear phase decomposition of images. Zbl 07123013
Li, Yanting; Zhang, Liming; Qian, Tao
2019
Schwarz problems for poly-Hardy space on the unit ball. Zbl 1384.30009
Kähler, Uwe; Ku, Min; Qian, Tao
2017
Uncertainty principle and phase-amplitude analysis of signals on the unit sphere. Zbl 1386.94025
Dang, Pei; Qian, Tao; Chen, Qiuhui
2017
Hardy-Hodge decomposition of vector fields in $$\mathbb {R}^n$$. Zbl 1385.42018
Baratchart, Laurent; Dang, Pei; Qian, Tao
2018
On the inversion of Fueter’s theorem. Zbl 1348.30027
Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene
2016
An enhancement algorithm for cyclic adaptive Fourier decomposition. Zbl 1426.41012
Qian, Tao; Wang, Jianzhong; Mai, Weixiong
2019
Support vector machine adapted Tikhonov regularization method to solve Dirichlet problem. Zbl 1337.65172
Mo, Yan; Qian, Tao
2014
Backward shift invariant subspaces with applications to band preserving and phase retrieval problems. Zbl 1381.47006
Qian, Tao; Tan, Lihui
2016
Integral representations of a class of harmonic functions in the half space. Zbl 1329.35106
Zhang, Yan Hui; Deng, Guan Tie; Qian, Tao
2016
Stronger uncertainty principles for hypercomplex signals. Zbl 1342.42006
Yang, Yan; Dang, Pei; Qian, Tao
2015
Matching pursuits among shifted Cauchy kernels in higher-dimensional spaces. Zbl 1313.30164
Qian, Tao; Wang, Jinxun; Yang, Yan
2014
Approximation of monogenic functions by higher order Szegő kernels on the unit ball and half space. Zbl 1302.30068
Wang, Jinxun; Qian, Tao
2014
Spaces of harmonic functions with boundary values in $$Q^{\alpha}_{p,q}$$. Zbl 1307.42022
Yang, Qixiang; Qian, Tao; Li, Pengtao
2014
Mathematical theory of signal analysis vs. complex analysis method of harmonic analysis. Zbl 1299.42011
Qian, Tao; Zhang, Liming
2013
On sets of zeroes of Clifford algebra-valued polynomials. Zbl 1240.30215
Yang, Yan; Qian, Tao
2010
The inverse Fueter mapping theorem for axially monogenic functions of degree $$k$$. Zbl 1414.30050
Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene
2019
Fourier spectrum characterizations of $$H^{p}$$ spaces on tubes over cones for $$1\leq p \leq \infty$$. Zbl 06909439
Li, Hai-Chou; Deng, Guan-Tie; Qian, Tao
2018
Singular integrals and Fourier theory on Lipschitz boundaries. Zbl 1435.47001
Qian, Tao; Li, Pengtao
2019
Boundary value problems for periodic analytic functions. Zbl 1338.30027
Dang, Pei; Du, Jinyuan; Qian, Tao
2015
Space-frequency analysis in higher dimensions and applications. Zbl 1329.46038
Yang, Yan; Dang, Pei; Qian, Tao
2015
Sparse representation in Szegő kernels through reproducing kernel Hilbert space theory with applications. Zbl 1320.93036
Mo, Y.; Qian, T.; Mi, W.
2015
Extra-strong uncertainty principles in relation to phase derivative for signals in Euclidean spaces. Zbl 1366.94092
Dang, Pei; Qian, Tao; Yang, Yan
2016
Non-stretch mappings for a sharp estimate of the Beurling-Ahlfors operator. Zbl 1319.42010
Chen, Xingdi; Qian, Tao
2014
The AFD methods to compute Hilbert transform. Zbl 1325.42002
Mo, Yan; Qian, Tao; Mai, Weixiong; Chen, Qiuhui
2015
An elementary proof of the Paley–Wiener theorem in $$\mathbb C^m$$. Zbl 1211.32002
Yang, Y.; Qian, T.
2006
Fefferman-Stein decomposition for $$Q$$-spaces and micro-local quantities. Zbl 1350.42043
Yang, Qixiang; Qian, Tao; Li, Pengtao
2016
Greedy algorithms and rational approximation in one and several variables. Zbl 1388.30063
Baratchart, Laurent; Mai, Wei-Xiong; Qian, Tao
2016
Singular integrals with monogenic kernels on the $$m$$-torus and their Lipschitz perturbations. Zbl 0843.42007
Qian, Tao
1996
A holomorphic extension result. Zbl 0865.42008
Qian, Tao
1997
Two-dimensional frequency-domain system identification. Zbl 07256186
Wang, Xiaoyin; Qian, Tao; Leong, Iengtak; Gao, You
2020
Adaptive Fourier decompositions and rational approximations. I: Theory. Zbl 1304.65283
Qian, Tao
2014
Sampling error analysis and some properties of non-bandlimited signals that are reconstructed by generalized sinc functions. Zbl 1290.94024
Li, Youfa; Chen, Qiuhui; Qian, Tao; Wang, Yi
2014
$$L^{p}$$ polyharmonic Dirichlet problems in regular domains. III: The unit ball. Zbl 1295.31020
Du, Zhihua; Qian, Tao; Wang, Jinxun
2014
Two-dimensional frequency-domain system identification. Zbl 07256186
Wang, Xiaoyin; Qian, Tao; Leong, Iengtak; Gao, You
2020
A theory on non-constant frequency decompositions and applications. Zbl 07216537
Chen, Qiuhui; Qian, Tao; Tan, Lihui
2020
Fourier spectrum of Clifford $$H^p$$ spaces on $$\mathbb{R}_+^{n + 1}$$ for $$1 \leq p \leq \infty$$. Zbl 1432.42013
Dang, Pei; Mai, Weixiong; Qian, Tao
2020
AFD-based ILC designs in frequency domain for linear discrete-time systems. Zbl 07470749
Fu, Wen-Yuan; Li, Xiao-Dong; Qian, Tao
2020
2D partial unwinding – a novel non-linear phase decomposition of images. Zbl 07123013
Li, Yanting; Zhang, Liming; Qian, Tao
2019
An enhancement algorithm for cyclic adaptive Fourier decomposition. Zbl 1426.41012
Qian, Tao; Wang, Jianzhong; Mai, Weixiong
2019
The inverse Fueter mapping theorem for axially monogenic functions of degree $$k$$. Zbl 1414.30050
Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene
2019
Singular integrals and Fourier theory on Lipschitz boundaries. Zbl 1435.47001
Qian, Tao; Li, Pengtao
2019
A novel 2D partial unwinding adaptive Fourier decomposition method with application to frequency domain system identification. Zbl 1418.42008
Li, Yanting; Qian, Tao
2019
Hardy-Hodge decomposition of vector fields in $$\mathbb {R}^n$$. Zbl 1385.42018
Baratchart, Laurent; Dang, Pei; Qian, Tao
2018
Fourier spectrum characterizations of $$H^{p}$$ spaces on tubes over cones for $$1\leq p \leq \infty$$. Zbl 06909439
Li, Hai-Chou; Deng, Guan-Tie; Qian, Tao
2018
Characterizations of mono-components: the Blaschke and starlike types. Zbl 06916394
Qian, Tao; Tan, Lihui
2018
A novel Fourier theory on nonlinear phases and applications. Zbl 1424.32016
Qian, Tao
2018
Clifford coherent state transforms on spheres. Zbl 1431.81035
Dang, Pei; Mourão, José; Nunes, João P.; Qian, Tao
2018
Rational approximation in Hardy spaces on strips. Zbl 1407.30017
Mai, Weixiong; Qian, Tao
2018
Wavelets and holomorphic functions. Zbl 1397.30041
Qian, Tao; Yang, Qixiang
2018
Adaptive orthonormal systems for matrix-valued functions. Zbl 1370.47011
Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene
2017
Coherent state transforms and the Weyl equation in Clifford analysis. Zbl 1355.81076
Mourão, José; Nunes, João P.; Qian, Tao
2017
Adaptative decomposition: the case of the Drury-Arveson space. Zbl 06829778
Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene
2017
Aveiro method in reproducing kernel Hilbert spaces under complete dictionary. Zbl 1382.30005
Mai, Weixiong; Qian, Tao
2017
Schwarz problems for poly-Hardy space on the unit ball. Zbl 1384.30009
Kähler, Uwe; Ku, Min; Qian, Tao
2017
Uncertainty principle and phase-amplitude analysis of signals on the unit sphere. Zbl 1386.94025
Dang, Pei; Qian, Tao; Chen, Qiuhui
2017
Extracting outer function part from Hardy space function. Zbl 1395.30055
Tan, LiHui; Qian, Tao
2017
FFT formulations of adaptive Fourier decomposition. Zbl 1369.65184
Gao, You; Ku, Min; Qian, Tao; Wang, Jianzhong
2017
Adaptive Fourier decomposition-based Dirac type time-frequency distribution. Zbl 1369.94331
Zhang, Liming; Qian, Tao; Mai, Weixiong; Dang, Pei
2017
Rational approximation of functions in Hardy spaces. Zbl 1382.30069
Deng, Guantie; Li, Haichou; Qian, Tao
2017
The $$H^{\infty}$$ functional calculus based on the $$S$$-spectrum for quaternionic operators and for $$n$$-tuples of noncommuting operators. Zbl 1350.47017
Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene
2016
Extending coherent state transforms to Clifford analysis. Zbl 1349.81088
Kirwin, William D.; Mourão, José; Nunes, João P.; Qian, Tao
2016
Two-dimensional adaptive Fourier decomposition. Zbl 1347.42047
Qian, Tao
2016
Tighter uncertainty principles based on quaternion Fourier transform. Zbl 1338.42013
Yang, Yan; Dang, Pei; Qian, Tao
2016
Rational approximation of functions in Hardy spaces. Zbl 1353.30032
Deng, Guantie; Qian, Tao
2016
On the inversion of Fueter’s theorem. Zbl 1348.30027
Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene
2016
Backward shift invariant subspaces with applications to band preserving and phase retrieval problems. Zbl 1381.47006
Qian, Tao; Tan, Lihui
2016
Integral representations of a class of harmonic functions in the half space. Zbl 1329.35106
Zhang, Yan Hui; Deng, Guan Tie; Qian, Tao
2016
Extra-strong uncertainty principles in relation to phase derivative for signals in Euclidean spaces. Zbl 1366.94092
Dang, Pei; Qian, Tao; Yang, Yan
2016
Fefferman-Stein decomposition for $$Q$$-spaces and micro-local quantities. Zbl 1350.42043
Yang, Qixiang; Qian, Tao; Li, Pengtao
2016
Greedy algorithms and rational approximation in one and several variables. Zbl 1388.30063
Baratchart, Laurent; Mai, Wei-Xiong; Qian, Tao
2016
Hardy space decomposition of $$L^p$$ on the unit circle: $$0 < p \leq 1$$. Zbl 1342.30050
Li, Hai-Chou; Deng, Guan-Tie; Qian, Tao
2016
Consecutive minimum phase expansion of physically realizable signals with applications. Zbl 1332.30085
Mai, Weixiong; Dang, Pei; Zhang, Liming; Qian, Tao
2016
Basis pursuit for frequency-domain identification. Zbl 1382.93034
Mi, Wen; Qian, Tao; Li, Shuang
2016
Minimax principle and lower bounds in $$H^2$$-rational approximation. Zbl 1361.30057
Baratchart, Laurent; Chevillard, Sylvain; Qian, Tao
2016
Fueter mapping theorem in hypercomplex analysis. Zbl 1330.30005
Qian, Tao
2015
Estimation of hyperbolically partial derivatives of $$\rho$$-harmonic quasiconformal mappings and its applications. Zbl 1317.30025
Chen, Xingdi; Qian, Tao
2015
Stronger uncertainty principles for hypercomplex signals. Zbl 1342.42006
Yang, Yan; Dang, Pei; Qian, Tao
2015
Boundary value problems for periodic analytic functions. Zbl 1338.30027
Dang, Pei; Du, Jinyuan; Qian, Tao
2015
Space-frequency analysis in higher dimensions and applications. Zbl 1329.46038
Yang, Yan; Dang, Pei; Qian, Tao
2015
Sparse representation in Szegő kernels through reproducing kernel Hilbert space theory with applications. Zbl 1320.93036
Mo, Y.; Qian, T.; Mi, W.
2015
The AFD methods to compute Hilbert transform. Zbl 1325.42002
Mo, Yan; Qian, Tao; Mai, Weixiong; Chen, Qiuhui
2015
New aspects of Beurling-Lax shift invariant subspaces. Zbl 1338.94021
Tan, Lihui; Qian, Tao; Chen, Qiuhui
2015
Order filtrations of the edge algebra. Zbl 1328.58025
Lyu, Xiaojing; Qian, Tao; Schulze, B.-W.
2015
Corner boundary value problems. Zbl 1327.35476
Chang, Der-Chen; Qian, Tao; Schulze, Bert-Wolfgang
2015
A constructive proof of Beurling-Lax theorem. Zbl 1309.30045
Chen, Qiuhui; Qian, Tao
2015
Cyclic AFD algorithm for the best rational approximation. Zbl 1287.42018
Qian, Tao
2014
Rational orthogonal systems are Schauder bases. Zbl 1306.46023
Qian, Tao; Chen, Qiuhui; Tan, Lihui
2014
On backward shift algorithm for estimating poles of systems. Zbl 1296.93068
Mi, Wen; Qian, Tao
2014
Support vector machine adapted Tikhonov regularization method to solve Dirichlet problem. Zbl 1337.65172
Mo, Yan; Qian, Tao
2014
Matching pursuits among shifted Cauchy kernels in higher-dimensional spaces. Zbl 1313.30164
Qian, Tao; Wang, Jinxun; Yang, Yan
2014
Approximation of monogenic functions by higher order Szegő kernels on the unit ball and half space. Zbl 1302.30068
Wang, Jinxun; Qian, Tao
2014
Spaces of harmonic functions with boundary values in $$Q^{\alpha}_{p,q}$$. Zbl 1307.42022
Yang, Qixiang; Qian, Tao; Li, Pengtao
2014
Non-stretch mappings for a sharp estimate of the Beurling-Ahlfors operator. Zbl 1319.42010
Chen, Xingdi; Qian, Tao
2014
Adaptive Fourier decompositions and rational approximations. I: Theory. Zbl 1304.65283
Qian, Tao
2014
Sampling error analysis and some properties of non-bandlimited signals that are reconstructed by generalized sinc functions. Zbl 1290.94024
Li, Youfa; Chen, Qiuhui; Qian, Tao; Wang, Yi
2014
$$L^{p}$$ polyharmonic Dirichlet problems in regular domains. III: The unit ball. Zbl 1295.31020
Du, Zhihua; Qian, Tao; Wang, Jinxun
2014
How to catch smoothing properties and analyticity of functions by computers? Zbl 1328.65126
Castro, L. P.; Fujiwara, H.; Qian, T.; Saitoh, S.
2014
Adaptive Fourier decomposition and rational approximation. II: Software system design and development. Zbl 1303.65113
Zhang, Liming; Hong, Wei; Mai, Weixiong; Qian, Tao
2014
Optimal approximation by Blaschke forms. Zbl 1259.41021
Qian, Tao; Wegert, Elias
2013
A tighter uncertainty principle for linear canonical transform in terms of phase derivative. Zbl 1393.94205
Dang, Pei; Deng, Guan-Tie; Qian, Tao
2013
A sharper uncertainty principle. Zbl 1284.42019
Dang, Pei; Deng, Guan-Tie; Qian, Tao
2013
Comparison of adaptive mono-component decompositions. Zbl 1270.94041
Qian, Tao; Li, Hong; Stessin, Michael
2013
Remarks on adaptive Fourier decomposition. Zbl 1267.42006
Qian, Tao; Wang, Yanbo
2013
Transient time-frequency distribution based on mono-component decompositions. Zbl 1316.94025
Dang, Pei; Qian, Tao; Guo, Yuan Yuan
2013
Mathematical theory of signal analysis vs. complex analysis method of harmonic analysis. Zbl 1299.42011
Qian, Tao; Zhang, Liming
2013
Shannon-type sampling for multivariate non-bandlimited signals. Zbl 1283.94030
Chen, Qiuhui; Qian, Tao; Li, Youfa
2013
$$L^p$$ polyharmonic Dirichlet problems in regular domains. IV: The upper-half space. Zbl 1288.31004
Du, Zhihua; Qian, Tao; Wang, Jinxun
2013
Sufficient conditions for shift-invariant systems to be frames in $$L^2({\mathbb R^n})$$. Zbl 1272.42020
Li, Deng Feng; Qian, Tao
2013
Analytic sampling approximation by projection operator with application in decomposition of instantaneous frequency. Zbl 1279.41020
Li, Youfa; Qian, Tao
2013
Micro-local structure and two kinds of wavelet characterizations about the generalized Hardy spaces. Zbl 1284.42048
Yang, Qixiang; Qian, Tao
2013
Sparse reconstruction of Hardy signal and applications to time-frequency distribution. Zbl 1275.41017
Qian, Tao; Li, Shuang; Mai, Weixiong
2013
Frequency-domain identification: An algorithm based on an adaptive rational orthogonal system. Zbl 1244.93038
Mi, Wen; Qian, Tao
2012
A fast adaptive model reduction method based on Takenaka-Malmquist systems. Zbl 1256.93029
Mi, Wen; Qian, Tao; Wan, Feng
2012
Adaptive Fourier decomposition of functions in quaternionic Hardy spaces. Zbl 1254.30086
Qian, Tao; Sprößig, Wolfgang; Wang, Jinxun
2012
Hardy-Sobolev derivatives of phase and amplitude, and their applications. Zbl 1256.42012
Dang, Pei; Qian, Tao; Yang, Yan
2012
Phase derivative of monogenic signals in higher dimensional spaces. Zbl 1275.30027
Yang, Yan; Qian, Tao; Sommen, Frank
2012
$$L^p$$ polyharmonic Dirichlet problems in regular domains. II: The upper half plane. Zbl 1256.31002
Du, Zhihua; Qian, Tao; Wang, Jinxun
2012
Some remarks on the boundary behaviors of functions in the monogenic Hardy spaces. Zbl 1257.30057
Qian, Tao; Wang, Jinxun
2012
Adaptive Fourier series—a variation of greedy algorithm. Zbl 1214.30047
Qian, Tao; Wang, Yan-Bo
2011
Hardy-Sobolev spaces decomposition in signal analysis. Zbl 1211.30061
Dang, Pei; Qian, Tao; You, Zhong
2011
Algorithm of adaptive Fourier decomposition. Zbl 1393.94142
Qian, Tao; Zhang, Liming; Li, Zhixiong
2011
Analytic phase derivatives, all-pass filters and signals of minimum phase. Zbl 1392.94170
Dang, Pei; Qian, Tao
2011
Adaptive decomposition by weighted inner functions: a generalization of Fourier series. Zbl 1223.42006
Qian, Tao; Tan, Li-Hui; Wang, Yan-Bo
2011
Zeroes of slice monogenic functions. Zbl 1220.30071
Yang, Yan; Qian, Tao
2011
Zero-sets of Clifford analytic functions with real coefficients. Zbl 1249.30138
Yang, Yan; Qian, Tao
2011
A class of Fourier multipliers on starlike Lipschitz surfaces. Zbl 1232.42014
Li, Pengtao; Leong, Ieng Tak; Qian, Tao
2011
Intrinsic mono-component decomposition of functions: an advance of Fourier theory. Zbl 1188.42001
Qian, Tao
2010
Orthonormal bases with nonlinear phases. Zbl 1213.42126
Qian, Tao; Wang, Rui; Xu, Yuesheng; Zhang, Haizhang
2010
Adaptive decomposition of functions into pieces of non-negative instantaneous frequencies. Zbl 1200.94026
Qian, Tao; Ho, I. T.; Leong, I. T.; Wang, Yanbo
2010
On sets of zeroes of Clifford algebra-valued polynomials. Zbl 1240.30215
Yang, Yan; Qian, Tao
2010
Fixed trace {$$\beta$$}-Hermite ensembles: asymptotic eigenvalue density and the edge of the density. Zbl 1309.15056
Zhou, Da-Sheng; Liu, Dang-Zheng; Qian, Tao
2010
Fourier spectrum characterization of Hardy spaces and applications. Zbl 1169.42003
Qian, Tao; Xu, Yuesheng; Yan, Dunyan; Yan, Lixin; Yu, Bo
2009
Boundary derivatives of the phases of inner and outer functions and applications. Zbl 1173.31001
Qian, Tao
2009
...and 59 more Documents
all top 5

### Cited by 457 Authors

 125 Qian, Tao 27 Sabadini, Irene 26 Chen, Qiuhui 26 Colombo, Fabrizio 25 Dang, Pei 23 Sommen, Franciscus 15 Kähler, Uwe 15 Tan, Lihui 14 Deng, Guantie 14 Yang, Yan 13 Ku, Min 13 Mai, Weixiong 12 Li, Pingrun 11 Cerejeiras, Paula 11 Kou, Kit-Ian 11 Li, Youfa 10 Kraußhar, Rolf Sören 10 Peña Peña, Dixan 10 Wang, Jinxun 10 Yang, Lihua 9 Zhang, Liming 8 Alpay, Daniel Aron 8 Li, Luoqing 8 Li, Xingmin 8 Ren, Guangbin 7 Mi, Wen 7 Zhang, Haizhang 6 Diki, Kamal 6 Gantner, Jonathan 6 Vallarino, Maria 5 Axelsson, Andreas 5 Bernstein, Swanhild 5 Brackx, Fred F. 5 Constales, Denis 5 De Bie, Hendrik 5 Fei, Minggang 5 Fu, Yingxiong 5 Li, Haichou 5 Li, Pengtao 5 Liu, Mingsheng 5 McIntosh, Alan 5 Peng, Lizhong 5 Wang, Yanbo 4 Bahri, Mawardi 4 Baratchart, Laurent 4 De Schepper, Hennie 4 Du, Zhihua 4 Gu, Longfei 4 Huang, Chao 4 Liao, Jianquan 4 Pinton, Stefano 4 Qiao, Yuying 4 Schulze, Bert-Wolfgang 4 Sjogren, Peter 4 Wang, Daoshun 4 Wang, Yufeng 4 Zhang, Zhichao 3 Abdulhadi, Zayid 3 Ashino, Ryuichi 3 Auscher, Pascal 3 Coifman, Ronald Raphaël 3 Ding, Chao 3 Dong, Baohua 3 Gerhards, Christian 3 Ghanmi, Allal 3 González-Cervantes, José Óscar 3 Han, Deguang 3 Jefferies, Brian R. F. 3 Kimsey, David Patrick 3 Li, Chun 3 Li, Shanshan 3 Li, Shuang 3 Lin, Rongrong 3 Morais, João Pedro 3 Mourão, José 3 Nunes, João Pedro Vidal 3 Perotti, Alessandro 3 Qu, Wei 3 Saitoh, Saburou 3 Walter, Raymond 3 Wang, Ying 3 Wen, Zhihong 3 Yan, Dunyan 3 Yang, Qixiang 3 Yang, Shouzhi 3 Yuan, Hongfen 3 Zhang, Zhongxiang 2 Abreu-Blaya, Ricardo 2 Ahmad, Owais 2 Ali, Rosihan Mohamed 2 Banouh, Hicham 2 Ben Mabrouk, Anouar 2 Benahmadi, Abdelhadi 2 Bory Reyes, Juan 2 Pinheiro de Castro, Luís Filipe 2 Clausel, Marianne 2 Cui, Xiaona 2 De Knock, Bram 2 De Martino, Antonino 2 Delanghe, Richard ...and 357 more Authors
all top 5

### Cited in 119 Serials

 45 Advances in Applied Clifford Algebras 36 Complex Variables and Elliptic Equations 33 Mathematical Methods in the Applied Sciences 33 International Journal of Wavelets, Multiresolution and Information Processing 27 Journal of Mathematical Analysis and Applications 26 Complex Analysis and Operator Theory 15 The Journal of Fourier Analysis and Applications 12 Applied Mathematics and Computation 12 Science China. Mathematics 10 Journal of Mathematical Physics 9 Journal of Functional Analysis 6 Journal of Computational and Applied Mathematics 6 Results in Mathematics 6 Transactions of the American Mathematical Society 6 Zeitschrift für Analysis und ihre Anwendungen 6 The Journal of Geometric Analysis 6 Applied and Computational Harmonic Analysis 6 Acta Mathematica Sinica. English Series 5 Journal of Geometry and Physics 5 Numerical Functional Analysis and Optimization 5 Abstract and Applied Analysis 5 Journal of Inequalities and Applications 4 Applicable Analysis 4 Arkiv för Matematik 4 Proceedings of the American Mathematical Society 4 Journal of Integral Equations and Applications 4 Science in China. Series A 4 SIAM Journal on Mathematical Analysis 4 Computational Methods and Function Theory 3 Computers & Mathematics with Applications 3 Israel Journal of Mathematics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Automatica 3 Mathematische Nachrichten 3 Advances in Computational Mathematics 3 Integral Transforms and Special Functions 3 Journal of Pseudo-Differential Operators and Applications 3 Journal of Function Spaces 2 Journal of Approximation Theory 2 Journal of Differential Equations 2 Mathematische Zeitschrift 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Systems & Control Letters 2 Chinese Annals of Mathematics. Series B 2 Applied Mathematics Letters 2 Multidimensional Systems and Signal Processing 2 Acta Mathematica Sinica. New Series 2 Journal of Mathematical Imaging and Vision 2 Applied Mathematics. Series B (English Edition) 2 Calculus of Variations and Partial Differential Equations 2 Filomat 2 Journal of the Australian Mathematical Society 2 Mediterranean Journal of Mathematics 2 Boundary Value Problems 2 Journal of Physics A: Mathematical and Theoretical 2 Banach Journal of Mathematical Analysis 2 Analysis and Mathematical Physics 2 Journal of Applied Analysis and Computation 2 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 Acta Mechanica 1 Analysis Mathematica 1 Communications in Mathematical Physics 1 Journal d’Analyse Mathématique 1 Journal of the Franklin Institute 1 Journal of Statistical Physics 1 Problems of Information Transmission 1 Rocky Mountain Journal of Mathematics 1 Studia Mathematica 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Canadian Journal of Mathematics 1 Collectanea Mathematica 1 International Journal of Mathematics and Mathematical Sciences 1 Integral Equations and Operator Theory 1 Inventiones Mathematicae 1 Journal of Number Theory 1 Memoirs of the American Mathematical Society 1 Monatshefte für Mathematik 1 Circuits, Systems, and Signal Processing 1 Physica D 1 Revista Matemática Iberoamericana 1 Journal of the American Mathematical Society 1 Forum Mathematicum 1 Signal Processing 1 Communications in Partial Differential Equations 1 Pattern Recognition 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Indagationes Mathematicae. New Series 1 Applicationes Mathematicae 1 Computational and Applied Mathematics 1 Journal of Difference Equations and Applications 1 Discrete and Continuous Dynamical Systems 1 Taiwanese Journal of Mathematics 1 Communications in Nonlinear Science and Numerical Simulation 1 Journal of Modern Optics 1 Differential Equations 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Applied Mathematics 1 Communications on Pure and Applied Analysis 1 Bulletin of the Brazilian Mathematical Society. New Series ...and 19 more Serials
all top 5

### Cited in 45 Fields

 237 Functions of a complex variable (30-XX) 156 Harmonic analysis on Euclidean spaces (42-XX) 79 Information and communication theory, circuits (94-XX) 47 Operator theory (47-XX) 46 Numerical analysis (65-XX) 43 Functional analysis (46-XX) 40 Partial differential equations (35-XX) 33 Several complex variables and analytic spaces (32-XX) 33 Approximations and expansions (41-XX) 30 Integral transforms, operational calculus (44-XX) 25 Linear and multilinear algebra; matrix theory (15-XX) 24 Potential theory (31-XX) 23 Integral equations (45-XX) 19 Global analysis, analysis on manifolds (58-XX) 16 Abstract harmonic analysis (43-XX) 14 Quantum theory (81-XX) 13 Systems theory; control (93-XX) 11 Topological groups, Lie groups (22-XX) 11 Special functions (33-XX) 11 Statistics (62-XX) 10 Number theory (11-XX) 10 Differential geometry (53-XX) 8 Probability theory and stochastic processes (60-XX) 6 Real functions (26-XX) 5 Ordinary differential equations (34-XX) 4 Nonassociative rings and algebras (17-XX) 4 Mechanics of particles and systems (70-XX) 4 Biology and other natural sciences (92-XX) 3 Computer science (68-XX) 3 Optics, electromagnetic theory (78-XX) 2 Field theory and polynomials (12-XX) 2 Difference and functional equations (39-XX) 2 Manifolds and cell complexes (57-XX) 2 Fluid mechanics (76-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Operations research, mathematical programming (90-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Sequences, series, summability (40-XX) 1 Mechanics of deformable solids (74-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)