Edit Profile (opens in new tab) De Bie, Hendrik Co-Author Distance Author ID: de-bie.hendrik Published as: De Bie, Hendrik; De Bie, H.; de Bie, H. more...less Homepage: https://cage.ugent.be/~hdebie/ External Links: MGP · ORCID · Google Scholar · MathOverflow · Twitter Documents Indexed: 81 Publications since 2007, including 5 Additional arXiv Preprints Co-Authors: 51 Co-Authors with 75 Joint Publications 696 Co-Co-Authors all top 5 Co-Authors 6 single-authored 18 Sommen, Franciscus 11 Vinet, Luc 8 Lian, Pan 8 Oste, Roy 8 Van der Jeugt, Joris 7 Genest, Vincent X. 6 Constales, Denis 6 Coulembier, Kevin 6 van de Vijver, Wouter 5 De Schepper, Nele 4 Brackx, Fred F. 4 De Schepper, Hennie 4 Eelbode, David 4 Somberg, Petr 3 Cnudde, Lander 3 Iliev, Plamen 3 Soucek, Vladimir 3 Wutzig, Michael 2 Bao, Gejun 2 Bisbo, Asmus K. 2 De Clercq, Hadewijch 2 Langlois-Rémillard, Alexis 2 Lemay, Jean-Michel 2 Mertens, Teppo 2 Roels, Matthias 1 Altavilla, Amedeo 1 Bao, Sijia 1 Barbier, Sigiswald 1 Bujack, Roxana 1 Ciubotaru, Dan 1 Claerebout, Sam 1 Crampé, Nicolas 1 De Martino, Marcelo 1 De Ridder, Hilde 1 Ell, Todd Anthony 1 Førsted, Bent 1 Holíková, Marie 1 Maes, Frederick 1 Ørsted, Bent 1 Peña Peña, Dixan 1 Ren, Guangbin 1 Rubrecht, K. 1 Sangwine, Stephen J. 1 Scheuermann, Gerik 1 Struppa, Daniele Carlo 1 Tsujimoto, Satoshi 1 Vâjiac, Adrian I. 1 Vajiac, Mihaela B. 1 Xu, Yuan 1 Yang, Ze 1 Zhedanov, Alexei S. all top 5 Serials 7 Journal of Physics A: Mathematical and Theoretical 4 Journal of Mathematical Analysis and Applications 4 Journal of Mathematical Physics 4 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 4 Complex Analysis and Operator Theory 3 Mathematical Methods in the Applied Sciences 3 Advances in Applied Clifford Algebras 2 Communications in Mathematical Physics 2 Letters in Mathematical Physics 2 Journal of Algebra 2 Journal of Approximation Theory 2 Constructive Approximation 2 IMRN. International Mathematics Research Notices 2 Annals of Physics 2 Potential Analysis 2 The Journal of Fourier Analysis and Applications 2 Complex Variables and Elliptic Equations 1 Physics Letters. A 1 Rocky Mountain Journal of Mathematics 1 Journal of Geometry and Physics 1 Advances in Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Applied Mathematics and Computation 1 Bulletin of the London Mathematical Society 1 Journal of Functional Analysis 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Nachrichten 1 Proceedings of the American Mathematical Society 1 Proceedings of the London Mathematical Society. Third Series 1 Transactions of the American Mathematical Society 1 Revista Matemática Iberoamericana 1 The Journal of Geometric Analysis 1 Journal of Mathematical Imaging and Vision 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Journal of Lie Theory 1 Integral Transforms and Special Functions all top 5 Fields 41 Functions of a complex variable (30-XX) 25 Special functions (33-XX) 22 Harmonic analysis on Euclidean spaces (42-XX) 20 Quantum theory (81-XX) 17 Nonassociative rings and algebras (17-XX) 12 Global analysis, analysis on manifolds (58-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 6 Integral transforms, operational calculus (44-XX) 6 Functional analysis (46-XX) 5 Topological groups, Lie groups (22-XX) 5 Partial differential equations (35-XX) 5 Abstract harmonic analysis (43-XX) 5 Operator theory (47-XX) 4 Associative rings and algebras (16-XX) 3 Group theory and generalizations (20-XX) 3 Potential theory (31-XX) 2 Combinatorics (05-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Difference and functional equations (39-XX) 2 Differential geometry (53-XX) 1 General algebraic systems (08-XX) 1 Field theory and polynomials (12-XX) 1 Real functions (26-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 66 Publications have been cited 740 times in 334 Documents Cited by ▼ Year ▼ Dunkl operators and a family of realizations of \(\mathfrak{osp}(1|2)\). Zbl 1276.33021 De Bie, H.; Ørsted, B.; Somberg, P.; Souček, V. 39 2012 Spherical harmonics and integration in superspace. Zbl 1143.30315 De Bie, H.; Sommen, F. 38 2007 On the Clifford-Fourier transform. Zbl 1237.30018 De Bie, Hendrik; Xu, Yuan 36 2011 Explicit formulas for the Dunkl dihedral kernel and the \((\kappa,a)\)-generalized Fourier kernel. Zbl 1382.65474 Constales, Denis; De Bie, Hendrik; Lian, Pan 36 2018 A higher rank Racah algebra and the \(\mathbb{Z}_2^n\) Laplace-Dunkl operator. Zbl 1382.81113 De Bie, Hendrik; Genest, Vincent X.; van de Vijver, Wouter; Vinet, Luc 35 2018 Clifford algebras, Fourier transforms, and quantum mechanics. Zbl 1259.42001 De Bie, H. 30 2012 The \(\mathbb{Z}_2^n\) Dirac-Dunkl operator and a higher rank Bannai-Ito algebra. Zbl 1348.81253 De Bie, Hendrik; Genest, Vincent X.; Vinet, Luc 29 2016 A Dirac-Dunkl equation on \(S^2\) and the Bannai-Ito algebra. Zbl 1338.22011 De Bie, Hendrik; Genest, Vincent X.; Vinet, Luc 27 2016 The higher rank \(q\)-deformed Bannai-Ito and Askey-Wilson algebra. Zbl 1472.16025 De Bie, Hendrik; De Clercq, Hadewijch; van de Vijver, Wouter 24 2020 Correct rules for Clifford calculus on superspace. Zbl 1129.30034 De Bie, Hendrik; Sommen, Frank 22 2007 The class of Clifford-Fourier transforms. Zbl 1237.30017 De Bie, Hendrik; De Schepper, Nele; Sommen, Frank 21 2011 Convolution products for hypercomplex Fourier transforms. Zbl 1292.42007 Bujack, Roxana; De Bie, Hendrik; De Schepper, Nele; Scheuermann, Gerik 19 2014 Spherical harmonics and integration in superspace: II. Zbl 1179.30053 De Bie, H.; Eelbode, D.; Sommen, F. 18 2009 Integration in superspace using distribution theory. Zbl 1187.58011 Coulembier, K.; de Bie, H.; Sommen, F. 16 2009 Generalized Fourier transforms arising from the enveloping algebras of \(\mathfrak{sl}(2)\) and \(\mathfrak{osp}(1| 2\)). Zbl 1404.43010 De Bie, Hendrik; Oste, Roy; Van der Jeugt, Joris 16 2016 A Clifford analysis approach to superspace. Zbl 1132.81017 De Bie, H.; Sommen, F. 15 2007 A new construction of the Clifford-Fourier kernel. Zbl 1365.42007 Constales, Denis; De Bie, Hendrik; Lian, Pan 15 2017 The kernel of the radially deformed Fourier transform. Zbl 1285.42011 De Bie, H. 15 2013 The Cauchy-Kowalewski product for bicomplex holomorphic functions. Zbl 1258.30023 De Bie, H.; Struppa, D. C.; Vajiac, A.; Vajiac, M. B. 13 2012 Conformal symmetries of the super Dirac operator. Zbl 1395.17018 Coulembier, Kevin; De Bie, Hendrik 13 2015 The higher spin Laplace operator. Zbl 1368.47035 De Bie, Hendrik; Eelbode, David; Roels, Matthias 13 2017 The fractional Clifford-Fourier transform. Zbl 1322.30018 De Bie, Hendrik; De Schepper, Nele 13 2012 Fundamental solutions for the super Laplace and Dirac operators and all their natural powers. Zbl 1143.30022 De Bie, H.; Sommen, F. 12 2008 A discrete realization of the higher rank Racah algebra. Zbl 1444.81019 De Bie, Hendrik; van de Vijver, Wouter 12 2020 Orthosymplectically invariant functions in superspace. Zbl 1312.46065 Coulembier, K.; De Bie, H.; Sommen, F. 11 2010 On the algebra of symmetries of Laplace and Dirac operators. Zbl 1397.81085 De Bie, Hendrik; Oste, Roy; Van der Jeugt, Joris 11 2018 Fourier transform and related integral transforms in superspace. Zbl 1149.30037 De Bie, H. 10 2008 Orthogonality of Hermite polynomials in superspace and Mehler type formulae. Zbl 1233.33004 Coulembier, Kevin; De Bie, Hendrik; Sommen, Frank 10 2011 A superintegrable model with reflections on \(S^{n-1}\) and the higher rank Bannai-Ito algebra. Zbl 1366.81171 De Bie, Hendrik; Genest, Vincent X.; Lemay, Jean-Michel; Vinet, Luc 10 2017 Fischer decompositions in superspace. Zbl 1168.58004 De Bie, H.; Sommen, F. 10 2008 The metaplectic Howe duality and polynomial solutions for the symplectic Dirac operator. Zbl 1279.30051 De Bie, Hendrik; Somberg, Petr; Souček, Vladimir 9 2014 Hermite and Gegenbauer polynomials in superspace using Clifford analysis. Zbl 1152.30052 De Bie, H.; Sommen, F. 8 2007 A Cauchy integral formula in superspace. Zbl 1179.30054 De Bie, H.; Sommen, F. 8 2009 The Clifford deformation of the Hermite semigroup. Zbl 1273.43007 De Bie, Hendrik; Førsted, Bent; Somberg, Petr; Souček, Vladimir 8 2013 Bannai-Ito algebras and the \(osp(1,2)\) superalgebra. Zbl 1390.17009 De Bie, Hendrik; Genest, Vincent X.; Van de Vijver, Wouter; Vinet, Luc 7 2017 Reproducing kernels for polynomial null-solutions of Dirac operators. Zbl 1354.30044 De Bie, H.; Sommen, F.; Wutzig, M. 7 2016 Connecting spatial and frequency domains for the quaternion Fourier transform. Zbl 1410.42012 De Bie, H.; De Schepper, N.; Ell, T. A.; Rubrecht, K.; Sangwine, S. J. 7 2015 The Racah algebra: an overview and recent results. Zbl 1497.81062 De Bie, Hendrik; Iliev, Plamen; van de Vijver, Wouter; Vinet, Luc 7 2021 Schrödinger equation with delta potential in superspace. Zbl 1221.81050 De Bie, Hendrik 6 2008 The total angular momentum algebra related to the \(\mathrm S_3\) Dunkl Dirac equation. Zbl 1384.81024 De Bie, Hendrik; Oste, Roy; Van der Jeugt, Joris 5 2018 The harmonic transvector algebra in two vector variables. Zbl 1355.42019 De Bie, Hendrik; Eelbode, David; Roels, Matthias 5 2017 Slice Segal-Bargmann transform. Zbl 1370.81089 Cnudde, L.; De Bie, H. 5 2017 Algebraic approach to slice monogenic functions. Zbl 1322.30017 Cnudde, Lander; De Bie, Hendrik; Ren, Guangbin 5 2015 Bargmann and Barut-Girardello models for the Racah algebra. Zbl 1406.81046 De Bie, Hendrik; Iliev, Plamen; Vinet, Luc 5 2019 The \(q\)-Bannai-Ito algebra and multivariate \((-q)\)-Racah and Bannai-Ito polynomials. Zbl 1468.33019 De Bie, Hendrik; De Clercq, Hadewijch 5 2021 On a chain of harmonic and monogenic potentials in Euclidean half-space. Zbl 1318.30077 Brackx, F.; De Bie, H.; De Schepper, H. 4 2014 Fourier transforms in Clifford analysis. Zbl 1329.42009 De Bie, Hendrik 4 2015 A Fock model and the Segal-Bargmann transform for the minimal representation of the orthosymplectic Lie superalgebra \(\mathfrak{osp}(m, 2 | 2n)\). Zbl 1484.17014 Barbier, Sigiswald; Claerebout, Sam; De Bie, Hendrik 4 2020 Discrete Clifford analysis: the one-dimensional setting. Zbl 1262.30051 De Bie, H.; De Ridder, H.; Sommen, F. 4 2012 The Dunkl kernel and intertwining operator for dihedral groups. Zbl 1466.44004 De Bie, Hendrik; Lian, Pan 4 2021 Clifford-Gegenbauer polynomials related to the Dunkl Dirac operator. Zbl 1227.30038 De Bie, H.; De Schepper, N. 3 2011 Basic aspects of symplectic Clifford analysis for the symplectic Dirac operator. Zbl 1367.53042 De Bie, Hendrik; Holíková, Marie; Somberg, Petr 3 2017 Slice Fourier transform and convolutions. Zbl 1378.30021 Cnudde, Lander; De Bie, Hendrik 3 2017 Representations of the Lie superalgebra \(\mathfrak{osp}(1|2n)\) with polynomial bases. Zbl 1489.17008 Bisbo, Asmus K.; De Bie, Hendrik; Van der Jeugt, Joris 3 2021 Generating functions of orthogonal polynomials in higher dimensions. Zbl 1293.42027 De Bie, Hendrik; Peña Peña, Dixan; Sommen, Frank 3 2014 Implementing zonal harmonics with the Fueter principle. Zbl 1460.30016 Altavilla, Amedeo; De Bie, Hendrik; Wutzig, Michael 3 2021 An alternative definition of the Hermite polynomials related to the Dunkl Laplacian. Zbl 1163.33315 De Bie, Hendrik 2 2008 Harmonic and monogenic potentials in low dimensional Euclidean half-space. Zbl 1300.30088 Brackx, F.; De Bie, H.; De Schepper, H. 2 2014 New results on the radially deformed Dirac operator. Zbl 1376.33018 De Bie, Hendrik; De Schepper, Nele; Eelbode, David 2 2017 The kernel of the generalized Clifford-Fourier transform and its generating function. Zbl 1364.44001 Lian, Pan; Bao, Gejun; De Bie, Hendrik; Constales, Denis 2 2017 Finite-dimensional representations of the symmetry algebra of the dihedral Dunkl-Dirac operator. Zbl 1498.16037 De Bie, Hendrik; Langlois-Rémillard, Alexis; Oste, Roy; Van der Jeugt, Joris 2 2022 Distributional boundary values of harmonic potentials in Euclidean half-space as fundamental solutions of convolution operators in Clifford analysis. Zbl 1272.30068 Brackx, Fred; De Bie, Hendrik; De Schepper, Hennie 2 2013 Hilbert space for quantum mechanics on superspace. Zbl 1317.35026 Coulembier, K.; De Bie, H. 1 2011 Symmetries of the \(S_3\) Dirac-Dunkl operator. Zbl 1409.22018 De Bie, Hendrik; Oste, Roy; Van der Jeugt, Joris 1 2018 Solutions for the Lévy-Leblond or parabolic Dirac equation and its generalizations. Zbl 1431.81056 Bao, Sijia; Constales, Denis; De Bie, Hendrik; Mertens, Teppo 1 2020 Dunkl intertwining operator for symmetric groups. Zbl 1489.33012 De Bie, Hendrik; Lian, Pan 1 2021 Finite-dimensional representations of the symmetry algebra of the dihedral Dunkl-Dirac operator. Zbl 1498.16037 De Bie, Hendrik; Langlois-Rémillard, Alexis; Oste, Roy; Van der Jeugt, Joris 2 2022 The Racah algebra: an overview and recent results. Zbl 1497.81062 De Bie, Hendrik; Iliev, Plamen; van de Vijver, Wouter; Vinet, Luc 7 2021 The \(q\)-Bannai-Ito algebra and multivariate \((-q)\)-Racah and Bannai-Ito polynomials. Zbl 1468.33019 De Bie, Hendrik; De Clercq, Hadewijch 5 2021 The Dunkl kernel and intertwining operator for dihedral groups. Zbl 1466.44004 De Bie, Hendrik; Lian, Pan 4 2021 Representations of the Lie superalgebra \(\mathfrak{osp}(1|2n)\) with polynomial bases. Zbl 1489.17008 Bisbo, Asmus K.; De Bie, Hendrik; Van der Jeugt, Joris 3 2021 Implementing zonal harmonics with the Fueter principle. Zbl 1460.30016 Altavilla, Amedeo; De Bie, Hendrik; Wutzig, Michael 3 2021 Dunkl intertwining operator for symmetric groups. Zbl 1489.33012 De Bie, Hendrik; Lian, Pan 1 2021 The higher rank \(q\)-deformed Bannai-Ito and Askey-Wilson algebra. Zbl 1472.16025 De Bie, Hendrik; De Clercq, Hadewijch; van de Vijver, Wouter 24 2020 A discrete realization of the higher rank Racah algebra. Zbl 1444.81019 De Bie, Hendrik; van de Vijver, Wouter 12 2020 A Fock model and the Segal-Bargmann transform for the minimal representation of the orthosymplectic Lie superalgebra \(\mathfrak{osp}(m, 2 | 2n)\). Zbl 1484.17014 Barbier, Sigiswald; Claerebout, Sam; De Bie, Hendrik 4 2020 Solutions for the Lévy-Leblond or parabolic Dirac equation and its generalizations. Zbl 1431.81056 Bao, Sijia; Constales, Denis; De Bie, Hendrik; Mertens, Teppo 1 2020 Bargmann and Barut-Girardello models for the Racah algebra. Zbl 1406.81046 De Bie, Hendrik; Iliev, Plamen; Vinet, Luc 5 2019 Explicit formulas for the Dunkl dihedral kernel and the \((\kappa,a)\)-generalized Fourier kernel. Zbl 1382.65474 Constales, Denis; De Bie, Hendrik; Lian, Pan 36 2018 A higher rank Racah algebra and the \(\mathbb{Z}_2^n\) Laplace-Dunkl operator. Zbl 1382.81113 De Bie, Hendrik; Genest, Vincent X.; van de Vijver, Wouter; Vinet, Luc 35 2018 On the algebra of symmetries of Laplace and Dirac operators. Zbl 1397.81085 De Bie, Hendrik; Oste, Roy; Van der Jeugt, Joris 11 2018 The total angular momentum algebra related to the \(\mathrm S_3\) Dunkl Dirac equation. Zbl 1384.81024 De Bie, Hendrik; Oste, Roy; Van der Jeugt, Joris 5 2018 Symmetries of the \(S_3\) Dirac-Dunkl operator. Zbl 1409.22018 De Bie, Hendrik; Oste, Roy; Van der Jeugt, Joris 1 2018 A new construction of the Clifford-Fourier kernel. Zbl 1365.42007 Constales, Denis; De Bie, Hendrik; Lian, Pan 15 2017 The higher spin Laplace operator. Zbl 1368.47035 De Bie, Hendrik; Eelbode, David; Roels, Matthias 13 2017 A superintegrable model with reflections on \(S^{n-1}\) and the higher rank Bannai-Ito algebra. Zbl 1366.81171 De Bie, Hendrik; Genest, Vincent X.; Lemay, Jean-Michel; Vinet, Luc 10 2017 Bannai-Ito algebras and the \(osp(1,2)\) superalgebra. Zbl 1390.17009 De Bie, Hendrik; Genest, Vincent X.; Van de Vijver, Wouter; Vinet, Luc 7 2017 The harmonic transvector algebra in two vector variables. Zbl 1355.42019 De Bie, Hendrik; Eelbode, David; Roels, Matthias 5 2017 Slice Segal-Bargmann transform. Zbl 1370.81089 Cnudde, L.; De Bie, H. 5 2017 Basic aspects of symplectic Clifford analysis for the symplectic Dirac operator. Zbl 1367.53042 De Bie, Hendrik; Holíková, Marie; Somberg, Petr 3 2017 Slice Fourier transform and convolutions. Zbl 1378.30021 Cnudde, Lander; De Bie, Hendrik 3 2017 New results on the radially deformed Dirac operator. Zbl 1376.33018 De Bie, Hendrik; De Schepper, Nele; Eelbode, David 2 2017 The kernel of the generalized Clifford-Fourier transform and its generating function. Zbl 1364.44001 Lian, Pan; Bao, Gejun; De Bie, Hendrik; Constales, Denis 2 2017 The \(\mathbb{Z}_2^n\) Dirac-Dunkl operator and a higher rank Bannai-Ito algebra. Zbl 1348.81253 De Bie, Hendrik; Genest, Vincent X.; Vinet, Luc 29 2016 A Dirac-Dunkl equation on \(S^2\) and the Bannai-Ito algebra. Zbl 1338.22011 De Bie, Hendrik; Genest, Vincent X.; Vinet, Luc 27 2016 Generalized Fourier transforms arising from the enveloping algebras of \(\mathfrak{sl}(2)\) and \(\mathfrak{osp}(1| 2\)). Zbl 1404.43010 De Bie, Hendrik; Oste, Roy; Van der Jeugt, Joris 16 2016 Reproducing kernels for polynomial null-solutions of Dirac operators. Zbl 1354.30044 De Bie, H.; Sommen, F.; Wutzig, M. 7 2016 Conformal symmetries of the super Dirac operator. Zbl 1395.17018 Coulembier, Kevin; De Bie, Hendrik 13 2015 Connecting spatial and frequency domains for the quaternion Fourier transform. Zbl 1410.42012 De Bie, H.; De Schepper, N.; Ell, T. A.; Rubrecht, K.; Sangwine, S. J. 7 2015 Algebraic approach to slice monogenic functions. Zbl 1322.30017 Cnudde, Lander; De Bie, Hendrik; Ren, Guangbin 5 2015 Fourier transforms in Clifford analysis. Zbl 1329.42009 De Bie, Hendrik 4 2015 Convolution products for hypercomplex Fourier transforms. Zbl 1292.42007 Bujack, Roxana; De Bie, Hendrik; De Schepper, Nele; Scheuermann, Gerik 19 2014 The metaplectic Howe duality and polynomial solutions for the symplectic Dirac operator. Zbl 1279.30051 De Bie, Hendrik; Somberg, Petr; Souček, Vladimir 9 2014 On a chain of harmonic and monogenic potentials in Euclidean half-space. Zbl 1318.30077 Brackx, F.; De Bie, H.; De Schepper, H. 4 2014 Generating functions of orthogonal polynomials in higher dimensions. Zbl 1293.42027 De Bie, Hendrik; Peña Peña, Dixan; Sommen, Frank 3 2014 Harmonic and monogenic potentials in low dimensional Euclidean half-space. Zbl 1300.30088 Brackx, F.; De Bie, H.; De Schepper, H. 2 2014 The kernel of the radially deformed Fourier transform. Zbl 1285.42011 De Bie, H. 15 2013 The Clifford deformation of the Hermite semigroup. Zbl 1273.43007 De Bie, Hendrik; Førsted, Bent; Somberg, Petr; Souček, Vladimir 8 2013 Distributional boundary values of harmonic potentials in Euclidean half-space as fundamental solutions of convolution operators in Clifford analysis. Zbl 1272.30068 Brackx, Fred; De Bie, Hendrik; De Schepper, Hennie 2 2013 Dunkl operators and a family of realizations of \(\mathfrak{osp}(1|2)\). Zbl 1276.33021 De Bie, H.; Ørsted, B.; Somberg, P.; Souček, V. 39 2012 Clifford algebras, Fourier transforms, and quantum mechanics. Zbl 1259.42001 De Bie, H. 30 2012 The Cauchy-Kowalewski product for bicomplex holomorphic functions. Zbl 1258.30023 De Bie, H.; Struppa, D. C.; Vajiac, A.; Vajiac, M. B. 13 2012 The fractional Clifford-Fourier transform. Zbl 1322.30018 De Bie, Hendrik; De Schepper, Nele 13 2012 Discrete Clifford analysis: the one-dimensional setting. Zbl 1262.30051 De Bie, H.; De Ridder, H.; Sommen, F. 4 2012 On the Clifford-Fourier transform. Zbl 1237.30018 De Bie, Hendrik; Xu, Yuan 36 2011 The class of Clifford-Fourier transforms. Zbl 1237.30017 De Bie, Hendrik; De Schepper, Nele; Sommen, Frank 21 2011 Orthogonality of Hermite polynomials in superspace and Mehler type formulae. Zbl 1233.33004 Coulembier, Kevin; De Bie, Hendrik; Sommen, Frank 10 2011 Clifford-Gegenbauer polynomials related to the Dunkl Dirac operator. Zbl 1227.30038 De Bie, H.; De Schepper, N. 3 2011 Hilbert space for quantum mechanics on superspace. Zbl 1317.35026 Coulembier, K.; De Bie, H. 1 2011 Orthosymplectically invariant functions in superspace. Zbl 1312.46065 Coulembier, K.; De Bie, H.; Sommen, F. 11 2010 Spherical harmonics and integration in superspace: II. Zbl 1179.30053 De Bie, H.; Eelbode, D.; Sommen, F. 18 2009 Integration in superspace using distribution theory. Zbl 1187.58011 Coulembier, K.; de Bie, H.; Sommen, F. 16 2009 A Cauchy integral formula in superspace. Zbl 1179.30054 De Bie, H.; Sommen, F. 8 2009 Fundamental solutions for the super Laplace and Dirac operators and all their natural powers. Zbl 1143.30022 De Bie, H.; Sommen, F. 12 2008 Fourier transform and related integral transforms in superspace. Zbl 1149.30037 De Bie, H. 10 2008 Fischer decompositions in superspace. Zbl 1168.58004 De Bie, H.; Sommen, F. 10 2008 Schrödinger equation with delta potential in superspace. Zbl 1221.81050 De Bie, Hendrik 6 2008 An alternative definition of the Hermite polynomials related to the Dunkl Laplacian. Zbl 1163.33315 De Bie, Hendrik 2 2008 Spherical harmonics and integration in superspace. Zbl 1143.30315 De Bie, H.; Sommen, F. 38 2007 Correct rules for Clifford calculus on superspace. Zbl 1129.30034 De Bie, Hendrik; Sommen, Frank 22 2007 A Clifford analysis approach to superspace. Zbl 1132.81017 De Bie, H.; Sommen, F. 15 2007 Hermite and Gegenbauer polynomials in superspace using Clifford analysis. Zbl 1152.30052 De Bie, H.; Sommen, F. 8 2007 all cited Publications top 5 cited Publications all top 5 Cited by 287 Authors 57 De Bie, Hendrik 38 Vinet, Luc 26 Sommen, Franciscus 15 Mejjaoli, Hatem 14 Crampé, Nicolas 12 Genest, Vincent X. 12 Lian, Pan 11 De Schepper, Hennie 11 Eelbode, David 11 Gaboriaud, Julien 11 Marquette, Ian 10 Yuan, Hongfen 10 Zhedanov, Alexei S. 9 Adán, Alí Guzmán 9 Costarelli, Danilo 9 Ding, Chao 9 Iliev, Plamen 9 Vinti, Gianluca 8 Hitzer, Eckhard 8 Sabadini, Irene 7 Ryan, John 7 van de Vijver, Wouter 7 Van der Jeugt, Joris 6 Ben Saïd, Salem 6 Brackx, Fred F. 6 Constales, Denis 6 Coulembier, Kevin 6 Frappat, Luc 6 Latini, Danilo 6 Poulain D’Andecy, Loïc 6 Zhang, Yaozhong 5 Ben Mabrouk, Anouar 5 Colombo, Fabrizio 5 De Schepper, Nele 5 Diki, Kamal 5 Fei, Minggang 5 Huang, Hau-wen 5 Oste, Roy 5 Qiao, Yuying 5 Raeymaekers, Tim 5 Ragoucy, Eric 5 Somberg, Petr 5 Vajiac, Mihaela B. 5 Walter, Raymond 4 Alpay, Daniel Aron 4 Baseilhac, Pascal 4 De Clercq, Hadewijch 4 De Ridder, Hilde 4 Deleaval, Luc 4 Kumar, Romesh 4 Negzaoui, Selma 4 Roels, Matthias 4 Soucek, Vladimir 4 Vieira, Nelson 4 Vinet, Stéphane 4 Xu, Yuan 4 Yang, Heju 4 Zaimi, Meri 3 Arfaoui, Sabrine 3 Bahri, Mawardi 3 Barbier, Sigiswald 3 Bujack, Roxana 3 Castro Perelman, Carlos 3 Chung, Won-Sang 3 Claerebout, Sam 3 Cnudde, Lander 3 El Kamel, Jamel 3 Faustino, Nelson José Rodrigues 3 Hassanabadi, Hassan 3 Janssens, Tim 3 Jday, Rim 3 Karachik, Valeriĭ Valentinovich 3 Langlois-Rémillard, Alexis 3 Lemay, Jean-Michel 3 Li, Shanshan 3 Mertens, Teppo 3 Peña Peña, Dixan 3 Ren, Guangbin 3 Saini, Heera 3 Scheuermann, Gerik 3 Struppa, Daniele Carlo 3 Wutzig, Michael 2 Banouh, Hicham 2 Bao, Gejun 2 Bisbo, Asmus K. 2 Boubatra, Mohamed Amine 2 Campoamor-Stursberg, Rutwig 2 Cattani, Carlo 2 Cerejeiras, Paula 2 Coroianu, Lucian C. 2 De Martino, Antonino 2 De Martino, Marcelo 2 Demni, Nizar 2 Dong, Shihai 2 Feng, Zhiming 2 Gal, Sorin Gheorghe 2 Ghanmi, Allal 2 Ghobber, Saifallah 2 Kähler, Uwe 2 Lávička, Roman ...and 187 more Authors all top 5 Cited in 88 Serials 46 Advances in Applied Clifford Algebras 23 Journal of Physics A: Mathematical and Theoretical 20 Journal of Mathematical Physics 15 Complex Analysis and Operator Theory 13 Journal of Mathematical Analysis and Applications 10 Letters in Mathematical Physics 10 Applied Mathematics and Computation 9 Mathematical Methods in the Applied Sciences 8 Journal of Pseudo-Differential Operators and Applications 7 Complex Variables and Elliptic Equations 6 Nuclear Physics. B 6 The Journal of Fourier Analysis and Applications 6 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 5 Communications in Mathematical Physics 5 Physics Letters. A 5 Proceedings of the American Mathematical Society 5 Annals of Physics 4 Journal of Geometry and Physics 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Journal of Algebra 4 Journal of Approximation Theory 4 Mathematische Nachrichten 4 Transactions of the American Mathematical Society 4 Constructive Approximation 4 Integral Transforms and Special Functions 4 Annales Henri Poincaré 3 Journal of Functional Analysis 3 Results in Mathematics 3 Advances in Applied Mathematics 3 The Journal of Geometric Analysis 3 Potential Analysis 3 Journal of Lie Theory 2 Analysis Mathematica 2 Advances in Mathematics 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Linear Algebra and its Applications 2 Journal of Mathematical Imaging and Vision 2 Mathematical Physics, Analysis and Geometry 2 Journal of High Energy Physics 2 Analysis and Applications (Singapore) 2 Analysis and Mathematical Physics 1 Modern Physics Letters A 1 International Journal of Theoretical Physics 1 Linear and Multilinear Algebra 1 Rocky Mountain Journal of Mathematics 1 Theoretical and Mathematical Physics 1 Reviews in Mathematical Physics 1 Chaos, Solitons and Fractals 1 Czechoslovak Mathematical Journal 1 Geometriae Dedicata 1 Information Sciences 1 The Journal of the Indian Mathematical Society. New Series 1 Journal of the London Mathematical Society. Second Series 1 Journal of Pure and Applied Algebra 1 Jnanabha 1 Numerical Functional Analysis and Optimization 1 Revista de la Unión Matemática Argentina 1 Chinese Annals of Mathematics. Series A 1 Acta Applicandae Mathematicae 1 Annals of Global Analysis and Geometry 1 Physica D 1 Revista Matemática Iberoamericana 1 International Journal of Mathematics 1 ELA. The Electronic Journal of Linear Algebra 1 The Ramanujan Journal 1 Nonlinear Dynamics 1 Abstract and Applied Analysis 1 Journal of Inequalities and Applications 1 Discrete Dynamics in Nature and Society 1 Communications of the Korean Mathematical Society 1 Mathematical Modelling and Analysis 1 Computational Methods and Function Theory 1 Journal of Algebra and its Applications 1 Analysis in Theory and Applications 1 International Journal of Wavelets, Multiresolution and Information Processing 1 Mediterranean Journal of Mathematics 1 Oberwolfach Reports 1 Boundary Value Problems 1 Banach Journal of Mathematical Analysis 1 Communications in Theoretical Physics 1 Science China. Mathematics 1 Symmetry 1 Forum of Mathematics, Sigma 1 Journal of Mathematics 1 Proceedings of the American Mathematical Society. Series B 1 Bollettino dell’Unione Matematica Italiana 1 Journal of Combinatorial Algebra all top 5 Cited in 50 Fields 103 Functions of a complex variable (30-XX) 93 Harmonic analysis on Euclidean spaces (42-XX) 90 Quantum theory (81-XX) 79 Special functions (33-XX) 64 Nonassociative rings and algebras (17-XX) 40 Operator theory (47-XX) 39 Linear and multilinear algebra; matrix theory (15-XX) 37 Integral transforms, operational calculus (44-XX) 26 Partial differential equations (35-XX) 24 Functional analysis (46-XX) 23 Global analysis, analysis on manifolds (58-XX) 18 Associative rings and algebras (16-XX) 17 Abstract harmonic analysis (43-XX) 16 Topological groups, Lie groups (22-XX) 15 Information and communication theory, circuits (94-XX) 14 Real functions (26-XX) 14 Dynamical systems and ergodic theory (37-XX) 14 Differential geometry (53-XX) 11 Group theory and generalizations (20-XX) 11 Approximations and expansions (41-XX) 8 Combinatorics (05-XX) 7 Number theory (11-XX) 7 Potential theory (31-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Ordinary differential equations (34-XX) 6 Difference and functional equations (39-XX) 6 Computer science (68-XX) 6 Relativity and gravitational theory (83-XX) 4 Integral equations (45-XX) 4 Geometry (51-XX) 4 Numerical analysis (65-XX) 3 Algebraic geometry (14-XX) 3 Manifolds and cell complexes (57-XX) 3 Probability theory and stochastic processes (60-XX) 2 Commutative algebra (13-XX) 2 Mechanics of particles and systems (70-XX) 2 Optics, electromagnetic theory (78-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Field theory and polynomials (12-XX) 1 Category theory; homological algebra (18-XX) 1 Measure and integration (28-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Convex and discrete geometry (52-XX) 1 Fluid mechanics (76-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) Citations by Year