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## Bernstein, Swanhild

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 Author ID: bernstein.swanhild Published as: Bernstein, S.; Bernstein, Swanhild External Links: MGP · Wikidata
 Documents Indexed: 69 Publications since 1991, including 6 Books
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#### Co-Authors

 38 single-authored 6 Ebert, Svend 6 Kähler, Uwe 5 Sommen, Franciscus 4 Cerejeiras, Paula 4 Schaeben, Helmut 3 Gürlebeck, Klaus 3 Hielscher, Ralf 2 He, Fuli 2 Heise, Bettina 2 Kraußhar, Rolf Sören 2 Ku, Min 2 Pesenson, Isaac Zalmanovich 2 Reinhardt, Martin 2 Reséndis Ocampo, Lino Feliciano 2 Sabadini, Irene 2 Tovar, Luis Manuel 1 Baaske, Franka 1 Bernardes, Gil 1 Bouchot, Jean-Luc 1 De Ridder, Hilde 1 De Schepper, Hennie 1 Eriksson, Sirkka-Liisa 1 Häuser, Sören 1 Keydel, Paul 1 Lanzani, Loredana 1 Qiao, Yuying 1 Riedel, Jens-Erik 1 Ryan, John Gerard 1 Schausberger, Stefan E. 1 Schufmann, Sandra 1 Stifter, David
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#### Serials

 7 Mathematical Methods in the Applied Sciences 6 Advances in Applied Clifford Algebras 3 Zeitschrift für Analysis und ihre Anwendungen 3 Complex Variables and Elliptic Equations 3 Trends in Mathematics 2 Complex Variables. Theory and Application 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 Journal d’Analyse Mathématique 1 Studia Mathematica 1 International Journal of Mathematics and Mathematical Sciences 1 Applied Mathematics Letters 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Journal of Difference Equations and Applications 1 The Journal of Fourier Analysis and Applications 1 Computational Methods and Function Theory 1 Sampling Theory in Signal and Image Processing 1 Journal of Concrete and Applicable Mathematics 1 Boundary Value Problems 1 Complex Analysis and Operator Theory 1 PAMM. Proceedings in Applied Mathematics and Mechanics
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#### Fields

 39 Functions of a complex variable (30-XX) 19 Partial differential equations (35-XX) 15 Harmonic analysis on Euclidean spaces (42-XX) 13 Integral transforms, operational calculus (44-XX) 12 Operator theory (47-XX) 6 Potential theory (31-XX) 6 Integral equations (45-XX) 5 Information and communication theory, circuits (94-XX) 4 General and overarching topics; collections (00-XX) 4 Several complex variables and analytic spaces (32-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Functional analysis (46-XX) 3 Numerical analysis (65-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Quantum theory (81-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Nonassociative rings and algebras (17-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Geometry (51-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH

43 Publications have been cited 169 times in 129 Documents Cited by Year
On the left linear Riemann problem in Clifford analysis. Zbl 0864.35024
Bernstein, Swanhild
1996
Function theory for Laplace and Dirac-Hodge operators in hyperbolic space. Zbl 1135.58013
Qiao, Yuying; Bernstein, Swanhild; Eriksson, Sirkka-Liisa; Ryan, John
2006
Generalized analytic signals in image processing: comparison, theory and applications. Zbl 1316.94020
Bernstein, Swanhild; Bouchot, Jean-Luc; Reinhardt, Martin; Heise, Bettina
2013
Szegő projections for Hardy spaces of monogenic functions and applications. Zbl 1009.30026
Bernstein, Swanhild; Lanzani, Loredana
2002
On solutions of a discretized heat equation in discrete Clifford analysis. Zbl 1283.39002
Baaske, F.; Bernstein, S.; De Ridder, H.; Sommen, F.
2014
Wavelets on $$S^{3}$$ and $$SO(3)$$ — Their construction, relation to each other and Radon transform of wavelets on $$SO(3)$$. Zbl 1201.42024
Bernstein, Swanhild; Ebert, Svend
2010
Spherical singular integrals, monogenic kernels and wavelets on the three-dimensional sphere. Zbl 1169.42015
Bernstein, Swanhild
2009
Factorization of the nonlinear Schrödinger equation and applications. Zbl 1119.30028
Bernstein, S.
2006
A one-dimensional Radon transform on SO(3) and its application to texture goniometry. Zbl 1077.44001
Bernstein, Swanhild; Schaeben, Helmut
2005
Fourier plane filtering revisited – analogies in optics and mathematics. Zbl 1346.78002
Heise, Bettina; Reinhardt, Martin; Schausberger, Stefan E.; Häuser, Sören; Bernstein, Swanhild; Stifter, David
2014
Kernel based wavelets on $$S^3$$. Zbl 1198.42034
Bernstein, S.; Ebert, S.
2010
The generalized totally geodesic Radon transform and its application to texture analysis. Zbl 1158.44001
Bernstein, Swanhild; Hielscher, Ralf; Schaeben, Helmut
2009
On a higher-dimensional Miura transform. Zbl 1018.30038
Bernstein, Swanhild; Gürlebeck, Klaus
1999
Riemann-Hilbert problems for monogenic functions in axially symmetric domains. Zbl 1332.30079
He, Fuli; Ku, Min; Kähler, Uwe; Sommen, Frank; Bernstein, Swanhild
2016
Harmonic $$Q_{p}$$-spaces. Zbl 1154.31005
Bernstein, Swanhild
2009
Carleson measure and monogenic functions. Zbl 1122.30030
Bernstein, S.; Cerejeiras, P.
2007
Dirichlet and Hardy spaces of harmonic and monogenic functions. Zbl 1102.30048
Bernstein, S.; Gürlebeck, K.; Reséndis O., L. F.; Tovar S., L. M.
2006
On the index of Clifford algebra valued singular integral operators and the left linear Riemann problem. Zbl 0919.47043
Bernstein, Swanhild
1998
Fractional Riesz-Hilbert-type transforms and associated monogenic signals. Zbl 1376.44004
Bernstein, Swanhild
2017
Generalized splines for Radon transform on compact Lie groups with applications to crystallography. Zbl 1306.65287
Bernstein, Swanhild; Ebert, Svend; Pesenson, Isaac Z.
2013
The quaternionic Riemann problem. Zbl 0947.30029
Bernstein, Swanhild
1999
Factorization of solutions of the Schrödinger equation. Zbl 0872.35027
Bernstein, Swanhild
1996
Analytic studies in unbounded domains with applications to quaternionic operator theory and elliptic boundary value problems. Zbl 0857.30040
Bernstein, Swanhild
1993
Elliptic boundary value problems in unbounded domains. Zbl 0835.35037
Bernstein, S.
1993
A fractional Dirac operator. Zbl 1394.47047
Bernstein, Swanhild
2016
The Radon transform on $$SO(3)$$: motivations generalizations, discretization. Zbl 1288.44002
Bernstein, Swanhild; Pesenson, Isaac Z.
2013
Wavelets invariant under finite reflection groups. Zbl 1191.30016
Bernardes, G.; Bernstein, S.; Cerejeiras, P.; Kähler, U.
2010
Multidimensional inverse-scattering and Clifford analysis. Zbl 1018.35063
Bernstein, S.
2002
Fundamental solutions for Dirac-type operators. Zbl 0871.30041
Bernstein, Swanhild
1996
Operator calculus for elliptic boundary value problems in unbounded domains. Zbl 0795.35012
Bernstein, S.
1991
Quasi-monogenic functions. Zbl 1401.30056
Bernstein, Swanhild
2018
Modern trends in hypercomplex analysis. Selected papers presented at the session on Clifford and quaternionic analysis at the 10th international ISAAC congress, University of Macau, China, August 3–8, 2015. Zbl 1359.30003
Bernstein, Swanhild (ed.); Kähler, Uwe (ed.); Sabadini, Irene (ed.); Sommen, Franciscus (ed.)
2016
A fractional Hilbert transform for 2D signals. Zbl 1368.42008
Bernstein, Swanhild
2014
The fractional monogenic signal. Zbl 1314.30094
Bernstein, Swanhild
2014
Hypercomplex analysis: new perspectives and applications. Selected papers presented at the session on Clifford and quaternionic analysis at the 9th congress of the International Society for Analysis, its Applications, and Computation (ISAAC), Krakow, Poland, August 5–9, 2013. Zbl 1300.30002
Bernstein, Swanhild (ed.); Kähler, Uwe (ed.); Sabadini, Irene (ed.); Sommen, Frank (ed.)
2014
Lax pairs for 3D spatial problems based on the Dirac operator. Zbl 1290.30056
Bernstein, S.; Cerejeiras, P.; Kähler, U.
2014
On the diffusion equation and diffusion wavelets on flat cylinders and the $$n$$-torus. Zbl 1215.35082
Bernstein, Swanhild; Ebert, Svend; Kraußhar, Rolf Sören
2011
Clifford continuous wavelet transforms in $${\mathcal C}\ell_{0,2}$$ and $${\mathcal C}\ell_{0,3}$$. Zbl 1163.42308
Bernstein, S.
2008
The Schrödinger equation and a multidimensional inverse scattering transform. Zbl 1016.35064
Bernstein, Swanhild
2002
Riemann-Hilbert problems in Clifford analysis. Zbl 1014.30030
Bernstein, Swanhild
2001
Integral equations and function spaces for boundary values of monogenic functions. Zbl 1142.30338
Bernstein, Swanhild
2001
Left-linear and nonlinear Riemann problems in Clifford analysis. Zbl 0896.45002
Bernstein, Swanhild
1998
A special class of pseudodifferential operators. Zbl 0729.35153
Bernstein, Swanhild
1992
Quasi-monogenic functions. Zbl 1401.30056
Bernstein, Swanhild
2018
Fractional Riesz-Hilbert-type transforms and associated monogenic signals. Zbl 1376.44004
Bernstein, Swanhild
2017
Riemann-Hilbert problems for monogenic functions in axially symmetric domains. Zbl 1332.30079
He, Fuli; Ku, Min; Kähler, Uwe; Sommen, Frank; Bernstein, Swanhild
2016
A fractional Dirac operator. Zbl 1394.47047
Bernstein, Swanhild
2016
Modern trends in hypercomplex analysis. Selected papers presented at the session on Clifford and quaternionic analysis at the 10th international ISAAC congress, University of Macau, China, August 3–8, 2015. Zbl 1359.30003
Bernstein, Swanhild (ed.); Kähler, Uwe (ed.); Sabadini, Irene (ed.); Sommen, Franciscus (ed.)
2016
On solutions of a discretized heat equation in discrete Clifford analysis. Zbl 1283.39002
Baaske, F.; Bernstein, S.; De Ridder, H.; Sommen, F.
2014
Fourier plane filtering revisited – analogies in optics and mathematics. Zbl 1346.78002
Heise, Bettina; Reinhardt, Martin; Schausberger, Stefan E.; Häuser, Sören; Bernstein, Swanhild; Stifter, David
2014
A fractional Hilbert transform for 2D signals. Zbl 1368.42008
Bernstein, Swanhild
2014
The fractional monogenic signal. Zbl 1314.30094
Bernstein, Swanhild
2014
Hypercomplex analysis: new perspectives and applications. Selected papers presented at the session on Clifford and quaternionic analysis at the 9th congress of the International Society for Analysis, its Applications, and Computation (ISAAC), Krakow, Poland, August 5–9, 2013. Zbl 1300.30002
Bernstein, Swanhild (ed.); Kähler, Uwe (ed.); Sabadini, Irene (ed.); Sommen, Frank (ed.)
2014
Lax pairs for 3D spatial problems based on the Dirac operator. Zbl 1290.30056
Bernstein, S.; Cerejeiras, P.; Kähler, U.
2014
Generalized analytic signals in image processing: comparison, theory and applications. Zbl 1316.94020
Bernstein, Swanhild; Bouchot, Jean-Luc; Reinhardt, Martin; Heise, Bettina
2013
Generalized splines for Radon transform on compact Lie groups with applications to crystallography. Zbl 1306.65287
Bernstein, Swanhild; Ebert, Svend; Pesenson, Isaac Z.
2013
The Radon transform on $$SO(3)$$: motivations generalizations, discretization. Zbl 1288.44002
Bernstein, Swanhild; Pesenson, Isaac Z.
2013
On the diffusion equation and diffusion wavelets on flat cylinders and the $$n$$-torus. Zbl 1215.35082
Bernstein, Swanhild; Ebert, Svend; Kraußhar, Rolf Sören
2011
Wavelets on $$S^{3}$$ and $$SO(3)$$ — Their construction, relation to each other and Radon transform of wavelets on $$SO(3)$$. Zbl 1201.42024
Bernstein, Swanhild; Ebert, Svend
2010
Kernel based wavelets on $$S^3$$. Zbl 1198.42034
Bernstein, S.; Ebert, S.
2010
Wavelets invariant under finite reflection groups. Zbl 1191.30016
Bernardes, G.; Bernstein, S.; Cerejeiras, P.; Kähler, U.
2010
Spherical singular integrals, monogenic kernels and wavelets on the three-dimensional sphere. Zbl 1169.42015
Bernstein, Swanhild
2009
The generalized totally geodesic Radon transform and its application to texture analysis. Zbl 1158.44001
Bernstein, Swanhild; Hielscher, Ralf; Schaeben, Helmut
2009
Harmonic $$Q_{p}$$-spaces. Zbl 1154.31005
Bernstein, Swanhild
2009
Clifford continuous wavelet transforms in $${\mathcal C}\ell_{0,2}$$ and $${\mathcal C}\ell_{0,3}$$. Zbl 1163.42308
Bernstein, S.
2008
Carleson measure and monogenic functions. Zbl 1122.30030
Bernstein, S.; Cerejeiras, P.
2007
Function theory for Laplace and Dirac-Hodge operators in hyperbolic space. Zbl 1135.58013
Qiao, Yuying; Bernstein, Swanhild; Eriksson, Sirkka-Liisa; Ryan, John
2006
Factorization of the nonlinear Schrödinger equation and applications. Zbl 1119.30028
Bernstein, S.
2006
Dirichlet and Hardy spaces of harmonic and monogenic functions. Zbl 1102.30048
Bernstein, S.; Gürlebeck, K.; Reséndis O., L. F.; Tovar S., L. M.
2006
A one-dimensional Radon transform on SO(3) and its application to texture goniometry. Zbl 1077.44001
Bernstein, Swanhild; Schaeben, Helmut
2005
Szegő projections for Hardy spaces of monogenic functions and applications. Zbl 1009.30026
Bernstein, Swanhild; Lanzani, Loredana
2002
Multidimensional inverse-scattering and Clifford analysis. Zbl 1018.35063
Bernstein, S.
2002
The Schrödinger equation and a multidimensional inverse scattering transform. Zbl 1016.35064
Bernstein, Swanhild
2002
Riemann-Hilbert problems in Clifford analysis. Zbl 1014.30030
Bernstein, Swanhild
2001
Integral equations and function spaces for boundary values of monogenic functions. Zbl 1142.30338
Bernstein, Swanhild
2001
On a higher-dimensional Miura transform. Zbl 1018.30038
Bernstein, Swanhild; Gürlebeck, Klaus
1999
The quaternionic Riemann problem. Zbl 0947.30029
Bernstein, Swanhild
1999
On the index of Clifford algebra valued singular integral operators and the left linear Riemann problem. Zbl 0919.47043
Bernstein, Swanhild
1998
Left-linear and nonlinear Riemann problems in Clifford analysis. Zbl 0896.45002
Bernstein, Swanhild
1998
On the left linear Riemann problem in Clifford analysis. Zbl 0864.35024
Bernstein, Swanhild
1996
Factorization of solutions of the Schrödinger equation. Zbl 0872.35027
Bernstein, Swanhild
1996
Fundamental solutions for Dirac-type operators. Zbl 0871.30041
Bernstein, Swanhild
1996
Analytic studies in unbounded domains with applications to quaternionic operator theory and elliptic boundary value problems. Zbl 0857.30040
Bernstein, Swanhild
1993
Elliptic boundary value problems in unbounded domains. Zbl 0835.35037
Bernstein, S.
1993
A special class of pseudodifferential operators. Zbl 0729.35153
Bernstein, Swanhild
1992
Operator calculus for elliptic boundary value problems in unbounded domains. Zbl 0795.35012
Bernstein, S.
1991
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#### Cited by 126 Authors

 19 Bernstein, Swanhild 15 Kähler, Uwe 12 Kraußhar, Rolf Sören 8 Cerejeiras, Paula 8 Iglewska-Nowak, Ilona 7 Constales, Denis 6 Gu, Longfei 6 Ku, Min 6 Sommen, Franciscus 6 Yang, Heju 5 Abreu-Blaya, Ricardo 5 Ahmed, Ahmed El-Sayed 5 Bory Reyes, Juan 5 Grob, Dennis 5 Xie, Yonghong 4 De Schepper, Hennie 4 Faustino, Nelson José Rodrigues 4 Gürlebeck, Klaus 4 Kravchenko, Vladislav V. 4 Qiao, Yuying 4 Sprößig, Wolfgang 3 Brackx, Fred F. 3 De Ridder, Hilde 3 Ebert, Svend 3 He, Fuli 3 Pesenson, Isaac Zalmanovich 3 Ryan, John Gerard 2 Delanghe, Richard 2 Eriksson, Sirkka-Liisa 2 Fu, Zunwei 2 Hielscher, Ralf 2 Kou, Kit-Ian 2 Li, Zunfeng 2 Raeymaekers, Tim 2 Razgulin, A. V. 2 Reséndis Ocampo, Lino Feliciano 2 Sazonova, Sofia V. 2 Schaeben, Helmut 2 Tovar, Luis Manuel 2 Vanegas, Judith C. 2 Vargas, Franklin 2 Yang, Yan 1 Abdalla, Mohamed 1 Aghdam, E. Abdi 1 Aluie, Hussein 1 Arfaoui, Sabrine 1 Avetisyan, Karen L. 1 Bahmann, H. 1 Bauer, Frank 1 Ben Mabrouk, Anouar 1 Bernardes, Gil 1 Biancalana, Fabio 1 Brackx, Freddy 1 Cattani, Carlo 1 Chuev, V. P. 1 Dang, Pei 1 de Almeida, Regina 1 De Knock, Bram 1 Du, Jinyuan 1 Dubinskiĭ, Yuliĭ Andreevich 1 Feichtinger, Hans Georg 1 Ferreira, Milton 1 Fleischmann, Oliver 1 Fokas, Athanassios S. 1 Fu, Yingxiong 1 Führ, Hartmut 1 Guo, Bingchan 1 Gutting, Martin 1 Hartmann, Stefan 1 Häuser, Sören 1 Hayward, Rosie 1 Heise, Bettina 1 Ilmavirta, Joonas 1 Jinyuan, Du 1 Kabir, M. M. 1 Kamal, Alaa 1 Khajeh, A. 1 Koma, A. Yousefi 1 Kravchenko, V. V. 1 Kuznetsov, Sergeĭ Petrovich 1 Lakew, Dejenie A. 1 Li, Xiumin 1 Liu, Mingsheng 1 Loya, Paul A. 1 Luo, Weiyu 1 Ma, Daowei 1 Martin, Mircea 1 Miss Paredes, Augusto Guadalupe 1 Mochalov, V. V. 1 Mostefaoui, Z. 1 Omran, Saleh 1 Orelma, Heikki 1 Peña Peña, Dixan 1 Ping, Duan 1 Pinotsis, Dimitrios A. 1 Plaksa, Sergiĭ Anatoliĭovych 1 Qian, Tao 1 Ramirez T., Marco P. 1 Reissig, Michael 1 Rodrigues, Maria Manuela ...and 26 more Authors
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#### Cited in 39 Serials

 22 Advances in Applied Clifford Algebras 16 Mathematical Methods in the Applied Sciences 13 Complex Variables and Elliptic Equations 7 Complex Analysis and Operator Theory 6 Applied and Computational Harmonic Analysis 5 Zeitschrift für Analysis und ihre Anwendungen 5 Computational Methods and Function Theory 4 Journal of Mathematical Analysis and Applications 4 The Journal of Fourier Analysis and Applications 4 Boundary Value Problems 3 Applied Mathematics and Computation 3 Results in Mathematics 3 GEM - International Journal on Geomathematics 2 Numerical Functional Analysis and Optimization 2 Integral Transforms and Special Functions 2 International Journal of Wavelets, Multiresolution and Information Processing 2 Mathematical Geosciences 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Computational and Applied Mathematics 1 Journal of Differential Equations 1 Proceedings of the American Mathematical Society 1 Transactions of the American Mathematical Society 1 Advances in Applied Mathematics 1 Revista Matemática Iberoamericana 1 Mathematical and Computer Modelling 1 The Journal of Geometric Analysis 1 Computational Mathematics and Mathematical Physics 1 Journal of Mathematical Imaging and Vision 1 Russian Mathematics 1 Applied Mathematics. Series B (English Edition) 1 Journal of Inverse and Ill-Posed Problems 1 Acta Mathematica Sinica. English Series 1 Communications in Nonlinear Science and Numerical Simulation 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Journal of Physics A: Mathematical and Theoretical 1 Journal of Function Spaces 1 Korean Journal of Mathematics
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#### Cited in 36 Fields

 88 Functions of a complex variable (30-XX) 27 Partial differential equations (35-XX) 24 Harmonic analysis on Euclidean spaces (42-XX) 13 Functional analysis (46-XX) 12 Integral transforms, operational calculus (44-XX) 10 Information and communication theory, circuits (94-XX) 8 Potential theory (31-XX) 8 Operator theory (47-XX) 8 Global analysis, analysis on manifolds (58-XX) 7 Integral equations (45-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Numerical analysis (65-XX) 5 Optics, electromagnetic theory (78-XX) 5 Quantum theory (81-XX) 4 Special functions (33-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Differential geometry (53-XX) 3 Number theory (11-XX) 3 Difference and functional equations (39-XX) 3 Fluid mechanics (76-XX) 3 Geophysics (86-XX) 2 Group theory and generalizations (20-XX) 2 Ordinary differential equations (34-XX) 2 Abstract harmonic analysis (43-XX) 2 Statistics (62-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Combinatorics (05-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Systems theory; control (93-XX)

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