Edit Profile (opens in new tab) Mhaskar, Hrushikesh N. Co-Author Distance Author ID: mhaskar.hrushikesh-n Published as: Mhaskar, H. N.; Mhaskar, Hrushikesh N.; Mhaskar, Hrushikesh more...less External Links: MGP Documents Indexed: 143 Publications since 1980, including 2 Books and 8 Additional arXiv Preprints 6 Contributions as Editor Co-Authors: 72 Co-Authors with 99 Joint Publications 2,150 Co-Co-Authors all top 5 Co-Authors 48 single-authored 16 Prestin, Jurgen 13 Chui, Charles Kam-tai 13 Saff, Edward Barry 8 Narcowich, Francis J. 8 Ward, Joseph Dinneen 6 Filbir, Frank-Dieter 5 Chandrasekaran, Shivkumar 5 Le Gia, Quoc Thong 5 Micchelli, Charles A. 5 Xu, Yuan 4 Blatt, Hans-Peter 4 Pereverzev, Sergei V. 3 Lubinsky, Doron S. 3 Poggio, Tomaso A. 3 Van der Walt, Maria D. 3 Zhou, Dingxuan 2 Cloninger, Alexander 2 Ganesh, Mahadevan 2 Leviatan, Dany 2 Li, Xin 2 Mayeli, Azita 2 Nevai, Paul G. 2 Pesenson, Isaac Zalmanovich 1 Alimov, Alexey R. 1 Andrievskii, Vladimir V. 1 Baratchart, Laurent 1 Batenkov, Dmitry 1 Berdysheva, Elena E. 1 Butzer, Paul Leo 1 Dahmen, Wolfgang A. 1 Demanet, Laurent 1 DeVore, Ronald A. 1 Donoho, David Leigh 1 Freud, Géza 1 Gorman, C. H. 1 Govil, Narenda Kumar 1 Gu, Ming 1 Guo, Adam 1 Hahm, Nahmwoo 1 Hesse, Kerstin 1 Jain, Pawan Kumar 1 Jayaraman Raghuram, Karthik 1 Jayaraman, K. R. 1 Jetter, Kurt 1 Mao, Tong 1 Martínez-Finkelshtein, Andrei 1 Mason, Eric 1 McKenna, Michael 1 Moffitt, Joseph 1 Mohapatra, Ram Narayan 1 Nashed, Zuhair 1 Naumova, Valeriya 1 Pai, Devidas V. 1 Pritsker, Igor E. 1 Putinar, Mihai 1 Sauer, Tomas 1 Schumaker, Larry L. 1 Semenov, Vasyl Yu. 1 Semenova, Evgeniya V. 1 Shvarts, Eugene 1 Sivakumar, N. R. 1 Sloan, Ian Hugh 1 Sommer, Manfred 1 Spencer, Richard G. 1 Strauss, Hans 1 Stylianopoulos, Nikos S. 1 Szabados, Jozsef 1 Tikhonov, Sergey Yur’evich 1 Totik, Vilmos 1 Varjú, Péter Pál 1 Zhuang, Xiaosheng 1 zu Castell, Wolfgang all top 5 Serials 15 Journal of Approximation Theory 14 Applied and Computational Harmonic Analysis 7 Journal of Complexity 7 Advances in Computational Mathematics 5 Mathematics of Computation 5 Constructive Approximation 4 Journal of Mathematical Analysis and Applications 4 Neural Networks 4 The Journal of Fourier Analysis and Applications 3 Journal of Computational Physics 3 Transactions of the American Mathematical Society 3 SIAM Journal on Mathematical Analysis 3 GEM - International Journal on Geomathematics 2 International Journal of Mathematics and Mathematical Sciences 2 Proceedings of the American Mathematical Society 2 SIAM Journal on Numerical Analysis 2 Advances in Applied Mathematics 2 Acta Mathematica Hungarica 2 Bulletin of the American Mathematical Society. New Series 2 ETNA. Electronic Transactions on Numerical Analysis 2 Applied and Numerical Harmonic Analysis 1 Inverse Problems 1 Arkiv för Matematik 1 Applied Mathematics and Computation 1 Canadian Mathematical Bulletin 1 Indian Journal of Mathematics 1 Journal of Computational and Applied Mathematics 1 Monatshefte für Mathematik 1 Numerical Functional Analysis and Optimization 1 Numerische Mathematik 1 SIAM Journal on Control and Optimization 1 Circuits, Systems, and Signal Processing 1 Approximation Theory and its Applications 1 Neural Computation 1 IBM Journal of Research and Development 1 Indagationes Mathematicae. New Series 1 Communications on Pure and Applied Analysis 1 Analysis and Applications (Singapore) 1 Series in Approximations and Decompositions 1 Pure and Applied Mathematics (Boca Raton) 1 Jaen Journal on Approximation 1 Bulletin of Mathematical Sciences all top 5 Fields 94 Approximations and expansions (41-XX) 58 Harmonic analysis on Euclidean spaces (42-XX) 29 Numerical analysis (65-XX) 14 Computer science (68-XX) 12 Functions of a complex variable (30-XX) 12 Information and communication theory, circuits (94-XX) 11 Special functions (33-XX) 8 Statistics (62-XX) 6 General and overarching topics; collections (00-XX) 6 Potential theory (31-XX) 4 Combinatorics (05-XX) 4 Functional analysis (46-XX) 4 Biology and other natural sciences (92-XX) 3 Real functions (26-XX) 3 Systems theory; control (93-XX) 2 Partial differential equations (35-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Geophysics (86-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 126 Publications have been cited 1,849 times in 945 Documents Cited by ▼ Year ▼ Where does the sup norm of a weighted polynomial live? (A generalization of incomplete polynomials). Zbl 0582.41009 Mhaskar, H. N.; Saff, E. B. 101 1985 Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature. Zbl 0980.76070 Mhaskar, H. N.; Narcowich, F. J.; Ward, J. D. 95 2001 Extremal problems for polynomials with exponential weights. Zbl 0546.41014 Mhaskar, H. N.; Saff, E. B. 83 1984 Approximation by superposition of sigmoidal and radial basis functions. Zbl 0763.41015 Mhaskar, H. N.; Micchelli, Charles A. 80 1992 Introduction to the theory of weighted polynomial approximation. Zbl 0948.41500 Mhaskar, H. N. 74 1996 Deep vs. shallow networks: an approximation theory perspective. Zbl 1355.68233 Mhaskar, H. N.; Poggio, T. 70 2016 Degree of approximation by neural and translation networks with a single hidden layer. Zbl 0885.42012 Mhaskar, H. N.; Micchelli, Charles A. 57 1995 Approximation properties of a multilayered feedforward artificial neural network. Zbl 0824.41011 Mhaskar, H. N. 54 1993 A proof of Freud’s conjecture for exponential weights. Zbl 0653.42024 Lubinsky, D. S.; Mhaskar, H. N.; Saff, E. B. 51 1988 Diffusion polynomial frames on metric measure spaces. Zbl 1242.42027 Maggioni, M.; Mhaskar, H. N. 48 2008 Marcinkiewicz-Zygmund measures on manifolds. Zbl 1235.58007 Filbir, F.; Mhaskar, H. N. 43 2011 Localized linear polynomial operators and quadrature formulas on the sphere. Zbl 1190.65039 Le Gia, Q. T.; Mhaskar, H. N. 40 2009 A quadrature formula for diffusion polynomials corresponding to a generalized heat kernel. Zbl 1204.41005 Filbir, F.; Mhaskar, H. N. 40 2010 Approximation properties of zonal function networks using scattered data on the sphere. Zbl 0939.41012 Mhaskar, H. N.; Narcowich, F. J.; Ward, J. D. 35 1999 On trigonometric wavelets. Zbl 0780.42020 Chui, C. K.; Mhaskar, H. N. 33 1993 Neural networks for localized approximation. Zbl 0806.41020 Chui, C. K.; Li, Xin; Mhaskar, H. N. 33 1994 On the distribution of zeros of polynomials orthogonal on the unit circle. Zbl 0721.42014 Mhaskar, H. N.; Saff, E. B. 32 1990 On the detection of singularities of a periodic function. Zbl 0937.42014 Mhaskar, H. N.; Prestin, J. 31 2000 Eignets for function approximation on manifolds. Zbl 1201.41003 Mhaskar, H. N. 30 2010 Fundamentals of approximation theory. Zbl 0964.41001 Mhaskar, Hrushikesh N.; Pai, Devidas V. 27 2000 \(L^p\) Bernstein estimates and approximation by spherical basis functions. Zbl 1200.41019 Mhaskar, H. N.; Narcowich, F. J.; Prestin, J.; Ward, J. D. 25 2010 On the tractability of multivariate integration and approximation by neural networks. Zbl 1344.65036 Mhaskar, H. N. 24 2004 Weighted quadrature formulas and approximation by zonal function networks on the sphere. Zbl 1103.65028 Mhaskar, H. N. 24 2006 On the representation of smooth functions on the sphere using finitely many bits. Zbl 1082.41020 Mhaskar, H. N. 24 2005 Bounds for certain Freud-type orthogonal polynomials. Zbl 0716.42020 Mhaskar, H. N. 24 1990 Signal decomposition and analysis via extraction of frequencies. Zbl 1330.94013 Chui, Charles K.; Mhaskar, H. N. 24 2016 Polynomial frames: a fast tour. Zbl 1077.42028 Mhaskar, H. N.; Prestin, J. 23 2005 Weighted polynomial approximation. Zbl 0602.41004 Mhaskar, H. N. 21 1986 Polynomial operators and local smoothness classes on the unit interval. Zbl 1083.41004 Mhaskar, H. N. 21 2004 The distribution of zeros of asymptotically extremal polynomials. Zbl 0744.41007 Mhaskar, H. N.; Saff, E. B. 21 1991 Where does the L p-norm of a weighted polynomial live? Zbl 0636.41008 Mhaskar, H. N.; Saff, E. B. 20 1987 Limitations of the approximation capabilities of neural networks with one hidden layer. Zbl 0855.41026 Chui, C. K.; Li, Xin; Mhaskar, H. N. 20 1996 On the problem of parameter estimation in exponential sums. Zbl 1254.94015 Filbir, F.; Mhaskar, H. N.; Prestin, J. 18 2012 On local smoothness classes of periodic functions. Zbl 1096.42018 Mhaskar, H. N.; Prestin, J. 17 2005 Quadrature in Besov spaces on the Euclidean sphere. Zbl 1134.41013 Hesse, K.; Mhaskar, H. N.; Sloan, I. H. 17 2007 Weighted analogues of capacity, transfinite diameter, and Chebyshev constant. Zbl 0747.31001 Mhaskar, H. N.; Saff, E. B. 16 1992 When is approximation by Gaussian networks necessarily a linear process? Zbl 1084.68104 Mhaskar, H. N. 15 2004 Polynomial frames on the sphere. Zbl 0974.41004 Mhaskar, H. N.; Narcowich, F. J.; Prestin, J.; Ward, J. D. 14 2000 Dimension-independent bounds on the degree of approximation by neural networks. Zbl 0823.41012 Mhaskar, H. N.; Micchelli, C. A. 14 1994 Polynomial operators and local approximation of solutions of pseudo-differential equations on the sphere. Zbl 1090.65133 Le Gia, Q. T.; Mhaskar, H. N. 14 2006 Weighted polynomials on finite and infinite intervals: A unified approach. Zbl 0565.41017 Mhaskar, H. N.; Saff, E. B. 12 1984 A generalized diffusion frame for parsimonious representation of functions on data defined manifolds. Zbl 1222.42036 Mhaskar, H. N. 11 2011 Approximation with interpolatory constraints. Zbl 0993.41005 Mhaskar, H. N.; Narcowich, F. J.; Sivakumar, N.; Ward, J. D. 11 2002 On a filter for exponentially localized kernels based on Jacobi polynomials. Zbl 1203.42038 Filbir, F.; Mhaskar, H. N.; Prestin, J. 11 2009 Polynomial operators for spectral approximation of piecewise analytic functions. Zbl 1161.41008 Mhaskar, H. N.; Prestin, J. 11 2009 Minimum Sobolev norm interpolation with trigonometric polynomials on the torus. Zbl 1302.41001 Chandrasekaran, S.; Jayaraman, K. R.; Mhaskar, H. N. 11 2013 Representation of functions on big data: graphs and trees. Zbl 1329.62033 Chui, C. K.; Filbir, F.; Mhaskar, H. N. 11 2015 Extremal problems for polynomials with Laguerre weights. Zbl 0574.41014 Mhaskar, H. N.; Saff, E. B. 10 1983 A general discrepancy theorem. Zbl 0797.30032 Blatt, H.-P.; Mhaskar, H. N. 10 1993 Local quadrature formulas on the sphere. Zbl 1074.41025 Mhaskar, H. N. 9 2004 Representation of functions on big data associated with directed graphs. Zbl 1378.68134 Chui, Charles K.; Mhaskar, H. N.; Zhuang, Xiaosheng 9 2018 Data-driven atomic decomposition via frequency extraction of intrinsic mode functions. Zbl 1361.94023 Chui, Charles K.; Mhaskar, H. N.; van der Walt, Maria D. 9 2016 Weighted polynomial approximation in rearrangement invariant Banach function spaces on the whole real line. Zbl 0516.41004 Freud, G.; Mhaskar, H. N. 8 1980 A Markov-Bernstein inequality for Gaussian networks. Zbl 1077.41011 Mhaskar, H. N. 8 2005 Freud’s conjecture for exponential weights. Zbl 0606.42018 Lubinsky, D. S.; Mhaskar, H. N.; Saff, E. B. 8 1986 Local quadrature formulas on the sphere. II. Zbl 1098.41029 Mhaskar, H. N. 8 2004 Local numerical integration on the sphere. Zbl 1305.65106 Beckmann, J.; Mhaskar, H. N.; Prestin, J. 8 2014 The rate of monotone spline approximation in the \(L_p\)-norm. Zbl 0516.41010 Leviatan, D.; Mhaskar, H. N. 7 1982 On Marcinkiewicz-Zygmund-type inequalities. Zbl 0901.41011 Mhaskar, H. N.; Prestin, J. 7 1998 Polynomials with Laguerre weights in \(L^ p\). Zbl 0565.41018 Mhaskar, H. N.; Saff, E. B. 7 1984 A unified framework for harmonic analysis of functions on directed graphs and changing data. Zbl 1395.42066 Mhaskar, H. N. 7 2018 Polynomial frames for the detection of singularities. Zbl 0962.42020 Mhaskar, H. N.; Prestin, J. 7 2000 Polynomial operators and local smoothness classes on the unit interval. II. Zbl 1181.41047 Mhaskar, H. N. 7 2009 Smooth function extension based on high dimensional unstructured data. Zbl 1297.41002 Chui, Charles K.; Mhaskar, H. N. 7 2014 Approximation theory and neural networks. Zbl 1037.41011 Mhaskar, H. N. 7 2001 Function approximation by deep networks. Zbl 1442.62215 Mhaskar, H. N.; Poggio, T. 7 2020 Weighted polynomial approximation of entire functions. II. Zbl 0475.41003 Mhaskar, H. N. 6 1981 Neural networks for functional approximation and system identification. Zbl 0872.68153 Mhaskar, H. N.; Hahm, Nahmwoo 6 1997 Quadrature formulas for integration of multivariate trigonometric polynomials on spherical triangles. Zbl 1258.65028 Beckmann, J.; Mhaskar, H. N.; Prestin, J. 6 2012 Extensions of the Dirichlet-Jordan criterion to a general class of orthogonal polynomial expansions. Zbl 0545.42020 Mhaskar, H. N. 5 1984 Filtered Legendre expansion method for numerical differentiation at the boundary point with application to blood glucose predictions. Zbl 1334.65058 Mhaskar, Hrushikesh N.; Naumova, V.; Pereverzyev, S. V. 5 2013 On the degree of approximation in multivariate weighted approximation. Zbl 1068.41053 Mhaskar, H. N. 5 2003 On the representation of band limited functions using finitely many bits. Zbl 1010.41016 Mhaskar, H. N. 5 2002 Stable soft extrapolation of entire functions. Zbl 1421.65032 Batenkov, Dmitry; Demanet, Laurent; Mhaskar, Hrushikesh N. 5 2019 Approximate quadrature measures on data-defined spaces. Zbl 1405.65030 Mhaskar, Hrushikesh N. 5 2018 Some discrepancy theorems. Zbl 0656.41003 Mhaskar, H. N. 4 1987 Matrix-free interpolation on the sphere. Zbl 1119.33012 Ganesh, M.; Mhaskar, H. N. 4 2006 Weighted polynomial approximation of entire functions. I. Zbl 0489.41011 Mhaskar, H. N. 4 1982 On the domain of convergence of series in polynomials orthogonal with respect to general weight functions on the whole real line. Zbl 0556.30002 Mhaskar, H. N. 4 1984 Wiener type theorems for Jacobi series with nonnegative coefficients. Zbl 1250.42084 Mhaskar, H. N.; Tikhonov, S. 4 2012 The rate of convergence of expansions in Freud polynomials. Zbl 0698.41004 Mhaskar, H. N. 4 1988 Function approximation with zonal function networks with activation functions analogous to the rectified linear unit functions. Zbl 1409.41008 Mhaskar, H. N. 4 2019 A unified method for super-resolution recovery and real exponential-sum separation. Zbl 1414.85002 Chui, Charles K.; Mhaskar, H. N. 4 2019 A quantitative Dirichlet-Jordan type theorem for orthogonal polynomial expansions. Zbl 0634.42021 Mhaskar, H. N. 3 1988 Errata to “Where does the L p-norm of a weighted polynomial live?”. Zbl 0648.41005 Mhaskar, H. N.; Saff, E. B. 3 1988 Open problems in constructive function theory. Zbl 1107.41011 Baratchart, L.; Martínez-Finkelshtein, A.; Jimenez, D.; Lubinsky, D. S.; Mhaskar, H. N.; Pritsker, I.; Putinar, M.; Stylianopoulos, N.; Totik, V.; Varju, P.; Xu, Y. 3 2006 Weighted analogues of Nikolskij-type inequalities and their applications. Zbl 0512.42001 Mhaskar, H. N. 3 1983 Approximation of real functions using neural networks. Zbl 0839.65019 Mhaskar, H. N. 3 1994 A local discrepancy theorem. Zbl 1013.42017 Andrievskii, V. V.; Blatt, H.-P.; Mhaskar, H. N. 3 2001 Bounded quasi-interpolatory polynomial operators. Zbl 0920.42019 Mhaskar, H. N.; Prestin, J. 3 1999 On a build-up polynomial frame for the detection of singularities. Zbl 0992.42025 Mhaskar, H. N.; Prestin, J. 3 1999 A Weierstrass-type theorem for certain weighted polynomials. Zbl 0578.41007 Mhaskar, H. N.; Saff, E. B. 3 1985 Mean convergence of expansions in Freud-type orthogonal polynomials. Zbl 0737.42024 Mhaskar, H. N.; Xu, Y. 3 1991 Weighted polynomials, radial basis functions and potentials on locally compact spaces. Zbl 0744.31004 Mhaskar, H. N. 3 1991 Detection of singularities using segment approximation. Zbl 0766.41007 Grothmann, R.; Mhaskar, H. N. 3 1992 Hermite interpolation at the zeros of certain Freud-type orthogonal polynomials. Zbl 0782.41005 Mhaskar, H. N.; Xu, Y. 3 1992 Frames and other bases in abstract and function spaces. Novel methods in harmonic analysis. Volume 1. Zbl 1373.42002 3 2017 Local approximation using Hermite functions. Zbl 1369.41003 Mhaskar, H. N. 3 2017 A Fourier-invariant method for locating point-masses and computing their attributes. Zbl 1395.42071 Chui, Charles K.; Mhaskar, H. N. 3 2018 Quadrature-free quasi-interpolation on the sphere. Zbl 1160.42301 Ganesh, M.; Mhaskar, H. N. 2 2006 Local approximation of operators. Zbl 1510.41014 Mhaskar, H. N. 1 2023 Cautious active clustering. Zbl 1467.62114 Cloninger, A.; Mhaskar, H. N. 2 2021 A low discrepancy sequence on graphs. Zbl 1472.05136 Cloninger, A.; Mhaskar, H. N. 2 2021 Function approximation by deep networks. Zbl 1442.62215 Mhaskar, H. N.; Poggio, T. 7 2020 An analysis of training and generalization errors in shallow and deep networks. Zbl 1434.68513 Mhaskar, H. N.; Poggio, T. 2 2020 A direct approach for function approximation on data defined manifolds. Zbl 1475.68319 Mhaskar, H. N. 1 2020 Stable soft extrapolation of entire functions. Zbl 1421.65032 Batenkov, Dmitry; Demanet, Laurent; Mhaskar, Hrushikesh N. 5 2019 Function approximation with zonal function networks with activation functions analogous to the rectified linear unit functions. Zbl 1409.41008 Mhaskar, H. N. 4 2019 A unified method for super-resolution recovery and real exponential-sum separation. Zbl 1414.85002 Chui, Charles K.; Mhaskar, H. N. 4 2019 Super-resolution meets machine learning: approximation of measures. Zbl 1436.94018 Mhaskar, H. N. 1 2019 Representation of functions on big data associated with directed graphs. Zbl 1378.68134 Chui, Charles K.; Mhaskar, H. N.; Zhuang, Xiaosheng 9 2018 A unified framework for harmonic analysis of functions on directed graphs and changing data. Zbl 1395.42066 Mhaskar, H. N. 7 2018 Approximate quadrature measures on data-defined spaces. Zbl 1405.65030 Mhaskar, Hrushikesh N. 5 2018 A Fourier-invariant method for locating point-masses and computing their attributes. Zbl 1395.42071 Chui, Charles K.; Mhaskar, H. N. 3 2018 Frames and other bases in abstract and function spaces. Novel methods in harmonic analysis. Volume 1. Zbl 1373.42002 3 2017 Local approximation using Hermite functions. Zbl 1369.41003 Mhaskar, H. N. 3 2017 Recent applications of harmonic analysis to function spaces, differential equations, and data science. Novel methods in harmonic analysis. Volume 2. Zbl 1378.42001 2 2017 Deep vs. shallow networks: an approximation theory perspective. Zbl 1355.68233 Mhaskar, H. N.; Poggio, T. 70 2016 Signal decomposition and analysis via extraction of frequencies. Zbl 1330.94013 Chui, Charles K.; Mhaskar, H. N. 24 2016 Data-driven atomic decomposition via frequency extraction of intrinsic mode functions. Zbl 1361.94023 Chui, Charles K.; Mhaskar, H. N.; van der Walt, Maria D. 9 2016 Localized summability kernels for Jacobi expansions. Zbl 1440.42014 Mhaskar, H. N. 1 2016 Representation of functions on big data: graphs and trees. Zbl 1329.62033 Chui, C. K.; Filbir, F.; Mhaskar, H. N. 11 2015 A minimum Sobolev norm technique for the numerical discretization of PDEs. Zbl 1352.65480 Chandrasekaran, S.; Mhaskar, H. N. 2 2015 In memoriam: Hubert A. Berens (1936–2015). Zbl 1319.01021 Alimov, Alexey; Berdysheva, Elena; Butzer, Paul; zu Castell, Wolfgang; Dahmen, Wolfgang; DeVore, Ron; Filbir, Frank; Jetter, Kurt; Mhaskar, Hrushikesh; Nevai, Paul; Sauer, Tomas; Schumaker, Larry; Sommer, Manfred; Strauss, Hans; Xu, Yuan 2 2015 Local numerical integration on the sphere. Zbl 1305.65106 Beckmann, J.; Mhaskar, H. N.; Prestin, J. 8 2014 Smooth function extension based on high dimensional unstructured data. Zbl 1297.41002 Chui, Charles K.; Mhaskar, H. N. 7 2014 Minimum Sobolev norm interpolation with trigonometric polynomials on the torus. Zbl 1302.41001 Chandrasekaran, S.; Jayaraman, K. R.; Mhaskar, H. N. 11 2013 Filtered Legendre expansion method for numerical differentiation at the boundary point with application to blood glucose predictions. Zbl 1334.65058 Mhaskar, Hrushikesh N.; Naumova, V.; Pereverzyev, S. V. 5 2013 Applications of classical approximation theory to periodic basis function networks and computational harmonic analysis. Zbl 1281.93110 Mhaskar, Hrushikesh N.; Nevai, Paul; Shvarts, Eugene 1 2013 On the problem of parameter estimation in exponential sums. Zbl 1254.94015 Filbir, F.; Mhaskar, H. N.; Prestin, J. 18 2012 Quadrature formulas for integration of multivariate trigonometric polynomials on spherical triangles. Zbl 1258.65028 Beckmann, J.; Mhaskar, H. N.; Prestin, J. 6 2012 Wiener type theorems for Jacobi series with nonnegative coefficients. Zbl 1250.42084 Mhaskar, H. N.; Tikhonov, S. 4 2012 Marcinkiewicz-Zygmund measures on manifolds. Zbl 1235.58007 Filbir, F.; Mhaskar, H. N. 43 2011 A generalized diffusion frame for parsimonious representation of functions on data defined manifolds. Zbl 1222.42036 Mhaskar, H. N. 11 2011 A quadrature formula for diffusion polynomials corresponding to a generalized heat kernel. Zbl 1204.41005 Filbir, F.; Mhaskar, H. N. 40 2010 Eignets for function approximation on manifolds. Zbl 1201.41003 Mhaskar, H. N. 30 2010 \(L^p\) Bernstein estimates and approximation by spherical basis functions. Zbl 1200.41019 Mhaskar, H. N.; Narcowich, F. J.; Prestin, J.; Ward, J. D. 25 2010 MRA contextual-recovery extension of smooth functions on manifolds. Zbl 1198.94025 Chui, Charles K.; Mhaskar, H. N. 2 2010 Localized linear polynomial operators and quadrature formulas on the sphere. Zbl 1190.65039 Le Gia, Q. T.; Mhaskar, H. N. 40 2009 On a filter for exponentially localized kernels based on Jacobi polynomials. Zbl 1203.42038 Filbir, F.; Mhaskar, H. N.; Prestin, J. 11 2009 Polynomial operators for spectral approximation of piecewise analytic functions. Zbl 1161.41008 Mhaskar, H. N.; Prestin, J. 11 2009 Polynomial operators and local smoothness classes on the unit interval. II. Zbl 1181.41047 Mhaskar, H. N. 7 2009 Diffusion polynomial frames on metric measure spaces. Zbl 1242.42027 Maggioni, M.; Mhaskar, H. N. 48 2008 Quadrature in Besov spaces on the Euclidean sphere. Zbl 1134.41013 Hesse, K.; Mhaskar, H. N.; Sloan, I. H. 17 2007 On bounded interpolatory and quasi-interpolatory polynomial operators. Zbl 1194.41009 Mhaskar, H. N. 1 2007 Weighted quadrature formulas and approximation by zonal function networks on the sphere. Zbl 1103.65028 Mhaskar, H. N. 24 2006 Polynomial operators and local approximation of solutions of pseudo-differential equations on the sphere. Zbl 1090.65133 Le Gia, Q. T.; Mhaskar, H. N. 14 2006 Matrix-free interpolation on the sphere. Zbl 1119.33012 Ganesh, M.; Mhaskar, H. N. 4 2006 Open problems in constructive function theory. Zbl 1107.41011 Baratchart, L.; Martínez-Finkelshtein, A.; Jimenez, D.; Lubinsky, D. S.; Mhaskar, H. N.; Pritsker, I.; Putinar, M.; Stylianopoulos, N.; Totik, V.; Varju, P.; Xu, Y. 3 2006 Quadrature-free quasi-interpolation on the sphere. Zbl 1160.42301 Ganesh, M.; Mhaskar, H. N. 2 2006 On the representation of smooth functions on the sphere using finitely many bits. Zbl 1082.41020 Mhaskar, H. N. 24 2005 Polynomial frames: a fast tour. Zbl 1077.42028 Mhaskar, H. N.; Prestin, J. 23 2005 On local smoothness classes of periodic functions. Zbl 1096.42018 Mhaskar, H. N.; Prestin, J. 17 2005 A Markov-Bernstein inequality for Gaussian networks. Zbl 1077.41011 Mhaskar, H. N. 8 2005 On the tractability of multivariate integration and approximation by neural networks. Zbl 1344.65036 Mhaskar, H. N. 24 2004 Polynomial operators and local smoothness classes on the unit interval. Zbl 1083.41004 Mhaskar, H. N. 21 2004 When is approximation by Gaussian networks necessarily a linear process? Zbl 1084.68104 Mhaskar, H. N. 15 2004 Local quadrature formulas on the sphere. Zbl 1074.41025 Mhaskar, H. N. 9 2004 Local quadrature formulas on the sphere. II. Zbl 1098.41029 Mhaskar, H. N. 8 2004 On the representation of band-dominant functions on the sphere using finitely many bits. Zbl 1058.41019 Mhaskar, H. N.; Narcowich, F. J.; Ward, J. D. 1 2004 On the degree of approximation in multivariate weighted approximation. Zbl 1068.41053 Mhaskar, H. N. 5 2003 Approximation with interpolatory constraints. Zbl 0993.41005 Mhaskar, H. N.; Narcowich, F. J.; Sivakumar, N.; Ward, J. D. 11 2002 On the representation of band limited functions using finitely many bits. Zbl 1010.41016 Mhaskar, H. N. 5 2002 Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature. Zbl 0980.76070 Mhaskar, H. N.; Narcowich, F. J.; Ward, J. D. 95 2001 Approximation theory and neural networks. Zbl 1037.41011 Mhaskar, H. N. 7 2001 A local discrepancy theorem. Zbl 1013.42017 Andrievskii, V. V.; Blatt, H.-P.; Mhaskar, H. N. 3 2001 Representing and analyzing scattered data on spheres. Zbl 0990.42024 Mhaskar, H. N.; Narcowich, F. J.; Ward, J. D. 2 2001 On the detection of singularities of a periodic function. Zbl 0937.42014 Mhaskar, H. N.; Prestin, J. 31 2000 Fundamentals of approximation theory. Zbl 0964.41001 Mhaskar, Hrushikesh N.; Pai, Devidas V. 27 2000 Polynomial frames on the sphere. Zbl 0974.41004 Mhaskar, H. N.; Narcowich, F. J.; Prestin, J.; Ward, J. D. 14 2000 Polynomial frames for the detection of singularities. Zbl 0962.42020 Mhaskar, H. N.; Prestin, J. 7 2000 Quasi-interpolation in shift invariant spaces. Zbl 0981.41002 Mhaskar, H. N.; Narcowich, F. J.; Ward, J. D. 2 2000 Approximation properties of zonal function networks using scattered data on the sphere. Zbl 0939.41012 Mhaskar, H. N.; Narcowich, F. J.; Ward, J. D. 35 1999 Bounded quasi-interpolatory polynomial operators. Zbl 0920.42019 Mhaskar, H. N.; Prestin, J. 3 1999 On a build-up polynomial frame for the detection of singularities. Zbl 0992.42025 Mhaskar, H. N.; Prestin, J. 3 1999 On a sequence of fast decreasing polynomial operators. Zbl 0943.41008 Mhaskar, Hrushikesh N.; Prestin, Jürgen 2 1999 On Marcinkiewicz-Zygmund-type inequalities. Zbl 0901.41011 Mhaskar, H. N.; Prestin, J. 7 1998 Neural networks for functional approximation and system identification. Zbl 0872.68153 Mhaskar, H. N.; Hahm, Nahmwoo 6 1997 Introduction to the theory of weighted polynomial approximation. Zbl 0948.41500 Mhaskar, H. N. 74 1996 Limitations of the approximation capabilities of neural networks with one hidden layer. Zbl 0855.41026 Chui, C. K.; Li, Xin; Mhaskar, H. N. 20 1996 Degree of approximation by neural and translation networks with a single hidden layer. Zbl 0885.42012 Mhaskar, H. N.; Micchelli, Charles A. 57 1995 A discrepancy theorem concerning polynomials of best approximation in \(L^ p_ w [-1, 1]\). Zbl 0831.41005 Blatt, H.-P.; Mhaskar, H. N. 1 1995 Neural networks for localized approximation. Zbl 0806.41020 Chui, C. K.; Li, Xin; Mhaskar, H. N. 33 1994 Dimension-independent bounds on the degree of approximation by neural networks. Zbl 0823.41012 Mhaskar, H. N.; Micchelli, C. A. 14 1994 Approximation of real functions using neural networks. Zbl 0839.65019 Mhaskar, H. N. 3 1994 Approximation properties of a multilayered feedforward artificial neural network. Zbl 0824.41011 Mhaskar, H. N. 54 1993 On trigonometric wavelets. Zbl 0780.42020 Chui, C. K.; Mhaskar, H. N. 33 1993 A general discrepancy theorem. Zbl 0797.30032 Blatt, H.-P.; Mhaskar, H. N. 10 1993 Weighted polynomial approximation of entire functions on unbounded subsets of the complex plane. Zbl 0807.30023 Mhaskar, H. N. 2 1993 Approximation by superposition of sigmoidal and radial basis functions. Zbl 0763.41015 Mhaskar, H. N.; Micchelli, Charles A. 80 1992 Weighted analogues of capacity, transfinite diameter, and Chebyshev constant. Zbl 0747.31001 Mhaskar, H. N.; Saff, E. B. 16 1992 Detection of singularities using segment approximation. Zbl 0766.41007 Grothmann, R.; Mhaskar, H. N. 3 1992 Hermite interpolation at the zeros of certain Freud-type orthogonal polynomials. Zbl 0782.41005 Mhaskar, H. N.; Xu, Y. 3 1992 On multivariate robust stability. Zbl 0762.93065 Chui, Charles K.; Mhaskar, H. N. 1 1992 The distribution of zeros of asymptotically extremal polynomials. Zbl 0744.41007 Mhaskar, H. N.; Saff, E. B. 21 1991 Mean convergence of expansions in Freud-type orthogonal polynomials. Zbl 0737.42024 Mhaskar, H. N.; Xu, Y. 3 1991 Weighted polynomials, radial basis functions and potentials on locally compact spaces. Zbl 0744.31004 Mhaskar, H. N. 3 1991 The convergence of Fourier series and a K-functional. Zbl 0731.42007 Mhaskar, H. N. 1 1991 On the distribution of zeros of polynomials orthogonal on the unit circle. Zbl 0721.42014 Mhaskar, H. N.; Saff, E. B. 32 1990 Bounds for certain Freud-type orthogonal polynomials. Zbl 0716.42020 Mhaskar, H. N. 24 1990 ...and 26 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,002 Authors 80 Mhaskar, Hrushikesh N. 54 Lubinsky, Doron S. 31 Saff, Edward Barry 19 Chui, Charles Kam-tai 17 Cao, Feilong 16 Prestin, Jurgen 16 Sloan, Ian Hugh 14 Costarelli, Danilo 14 Lin, Shaobo 13 Damelin, Steven Benjamin 12 Narcowich, Francis J. 12 Ward, Joseph Dinneen 12 Xu, Zongben 11 Potts, Daniel 11 Wang, Heping 11 Wang, Yuguang 10 Ehler, Martin 10 Filbir, Frank-Dieter 10 Kůrková, Věra 9 Gräf, Manuel 9 Pesenson, Isaac Zalmanovich 8 Brauchart, Johann S. 8 Jiang, Qingtang 8 Levin, Eli 8 Van Assche, Walter 8 Womersley, Robert S. 7 Chen, Yang 7 Dai, Feng 7 Ismail, Mourad El-Houssieny 7 Le Gia, Quoc Thong 7 Levin, A. L. 7 Li, Lin 7 Nevai, Paul G. 7 Petersen, Philipp Christian 7 Pritsker, Igor E. 7 Sanguineti, Marcello 7 Spigler, Renato 7 Totik, Vilmos 7 Yu, Dansheng 7 Zhou, Dingxuan 6 An, Congpei 6 Bello Hernández, Manuel 6 Ditzian, Zeev 6 Dragnev, Peter D. 6 Hesse, Kerstin 6 Horváth, Ágota P. 6 Kainen, Paul C. 6 Kunis, Stefan 6 Martínez-Finkelshtein, Andrei 6 Orive Rodríguez, Ramón Angel 6 Plonka, Gerlind 6 Sakai, Ryozi 6 Schwab, Christoph 6 Sheng, Baohuai 6 Zhuang, Xiaosheng 5 Alfaro, María Pilar 5 Blatt, Hans-Peter 5 Chen, Zhixiang 5 Cloninger, Alexander 5 Daubechies, Ingrid Chantal 5 Goh, Say Song 5 Grohs, Philipp 5 Hangelbroek, Thomas C. 5 Ismailov, Vugar E. 5 Jentzen, Arnulf 5 Kohler, Michael 5 Kuijlaars, Arno B. J. 5 Kutyniok, Gitta 5 Lu, Jian 5 Montaner, Jesús María 5 Occorsio, Donatella 5 Sandberg, Irwin W. 5 Shen, Zuowei 5 Sommariva, Alvise 5 Stylianopoulos, Nikos S. 5 Tikhonov, Sergey Yur’evich 5 Vianello, Marco 5 Vinti, Gianluca 5 Wu, Hao-Ning 5 Wu, Hau-Tieng 4 Anastassiou, George Angelos 4 Andrievskii, Vladimir V. 4 Aptekarev, Alexander Ivanovich 4 Batenkov, Dmitry 4 Díaz-Mendoza, Carlos 4 Erb, Wolfgang 4 Kwon, Kil Hyun 4 Li, Xin 4 López Lagomasino, Guillermo Tomás 4 Maiorov, Vitaly Evgen’evich 4 Mao, Tong 4 Mastroianni, Giuseppe 4 Narayan, Akil C. 4 Njåstad, Olav 4 Opschoor, Joost A. A. 4 Ortega-Cerdà, Joaquim 4 Pereverzev, Sergei V. 4 Poggio, Tomaso A. 4 Simon, Barry 4 Steinerberger, Stefan ...and 902 more Authors all top 5 Cited in 226 Serials 124 Journal of Approximation Theory 51 Applied and Computational Harmonic Analysis 48 Journal of Computational and Applied Mathematics 40 Constructive Approximation 32 Neural Networks 30 Journal of Mathematical Analysis and Applications 28 Journal of Complexity 24 Advances in Computational Mathematics 20 Mathematics of Computation 20 The Journal of Fourier Analysis and Applications 17 Applied Mathematics and Computation 16 Analysis and Applications (Singapore) 12 Computers & Mathematics with Applications 12 Acta Mathematica Hungarica 11 Proceedings of the American Mathematical Society 9 Numerical Functional Analysis and Optimization 9 GEM - International Journal on Geomathematics 8 Numerical Algorithms 7 Applied Numerical Mathematics 6 Journal of Functional Analysis 6 Results in Mathematics 6 Circuits, Systems, and Signal Processing 6 Neural Computation 6 The Journal of Geometric Analysis 6 Applied Mathematics. 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RACSAM 2 Statistics and Computing 2 Journal of Function Spaces 2 Advances in Data Science and Adaptive Analysis ...and 126 more Serials all top 5 Cited in 51 Fields 451 Approximations and expansions (41-XX) 279 Harmonic analysis on Euclidean spaces (42-XX) 253 Numerical analysis (65-XX) 153 Computer science (68-XX) 111 Special functions (33-XX) 77 Functions of a complex variable (30-XX) 74 Information and communication theory, circuits (94-XX) 53 Functional analysis (46-XX) 52 Statistics (62-XX) 42 Potential theory (31-XX) 38 Partial differential equations (35-XX) 36 Biology and other natural sciences (92-XX) 31 Probability theory and stochastic processes (60-XX) 27 Real functions (26-XX) 27 Operator theory (47-XX) 26 Combinatorics (05-XX) 23 Linear and multilinear algebra; matrix theory (15-XX) 19 Systems theory; control (93-XX) 15 Abstract harmonic analysis (43-XX) 15 Operations research, mathematical programming (90-XX) 14 Ordinary differential equations (34-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 14 Global analysis, analysis on manifolds (58-XX) 14 Statistical mechanics, structure of matter (82-XX) 13 Number theory (11-XX) 13 Integral equations (45-XX) 10 Sequences, series, summability (40-XX) 8 Difference and functional equations (39-XX) 7 Measure and integration (28-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Integral transforms, operational calculus (44-XX) 6 Mechanics of deformable solids (74-XX) 6 Quantum theory (81-XX) 6 Geophysics (86-XX) 5 Convex and discrete geometry (52-XX) 5 Optics, electromagnetic theory (78-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Algebraic geometry (14-XX) 4 Differential geometry (53-XX) 4 Fluid mechanics (76-XX) 3 General and overarching topics; collections (00-XX) 3 History and biography (01-XX) 3 Commutative algebra (13-XX) 2 Group theory and generalizations (20-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Geometry (51-XX) 2 General topology (54-XX) 2 Astronomy and astrophysics (85-XX) 1 Associative rings and algebras (16-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of particles and systems (70-XX) Citations by Year