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Researcher
Hendrik De Bie
Profile
Projects
Publications
Activities
Awards & Distinctions
106
Results
2024
Fourier Kernels Associated with the Clifford–Helmholtz System
Hendrik De Bie
Roy Oste
Ze Yang
U
Journal Article
in
Complex Analysis and Operator Theory
2024
2023
Generalised symmetries and bases for dunkl monogenics
Hendrik De Bie
Alexis Langlois-Rémillard
Roy Oste
Joris Van der Jeugt
A1
Journal Article
in
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
2023
Graphical calculus for quantum vertex operators
Hadewijch De Clercq
Hendrik De Bie
Jasper Stokman
Dissertation
2023
Hypercomplex algebra and sparse optimisation in multiband image processing
Srdan Lazendic
Hendrik De Bie
Aleksandra Pizurica
Dissertation
2023
Superspace realizations of the Bannai-Ito algebra
Nicolas Crampe
Hendrik De Bie
Plamen Iliev
Luc Vinet
A1
Journal Article
in
LETTERS IN MATHEMATICAL PHYSICS
2023
Topics in representation theory of the Dunkl total angular momentum algebra
Alexis Langlois-Rémillard
Joris Van der Jeugt
Hendrik De Bie
Roy Oste
Dissertation
2023
2022
A Lie algebra of Grassmannian Dirac operators and vector variables
Asmus Bisbo
Hendrik De Bie
Joris Van der Jeugt
A1
Journal Article
in
JOURNAL OF LIE THEORY
2022
Basis construction for representations of orthosymplectic algebras
Asmus Bisbo
Joris Van der Jeugt
Hendrik De Bie
Dissertation
2022
Finite-dimensional representations of the symmetry algebra of the dihedral Dunkl-Dirac operator
Hendrik De Bie
Alexis Langlois-Rémillard
Roy Oste
Joris Van der Jeugt
A1
Journal Article
in
JOURNAL OF ALGEBRA
2022
The monogenic Hua–Radon transform and its inverse
Denis Constales
Hendrik De Bie
Teppo Mertens
Franciscus Sommen
A1
Journal Article
in
JOURNAL OF GEOMETRIC ANALYSIS
2022
2021
Dunkl intertwining operator for symmetric groups
Hendrik De Bie
Pan Lian
A1
Journal Article
in
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
2021
Implementing zonal harmonics with the Fueter principle
Amedeo Altavilla
Hendrik De Bie
Michael Wutzig
A1
Journal Article
in
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
2021
On extending the ADMM algorithm to the quaternion algebra setting
Srdan Lazendic
Hendrik De Bie
Aleksandra Pizurica
C1
Conference
2021
Radon type transforms in Clifford analysis
Ren Hu
Hendrik De Bie
Tim Raeymaekers
Ali Guzmán Adán
Dissertation
2021
Representations of the Lie superalgebra osp(1 vertical bar 2n) with polynomial bases
Asmus Bisbo
Hendrik De Bie
Joris Van der Jeugt
A1
Journal Article
in
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
2021
Solving Racah problems through new algebraic structures
Wouter van de Vijver
Hendrik De Bie
Luc Vinet
Dissertation
2021
The Dunkl kernel and intertwining operator for dihedral groups
Hendrik De Bie
Pan Lian
A1
Journal Article
in
JOURNAL OF FUNCTIONAL ANALYSIS
2021
The Racah algebra : an overview and recent results
Hendrik De Bie
Plamen Iliev
Wouter van de Vijver
Luc Vinet
C1
Conference
2021
The Racah algebra and sln
Hendrik De Bie
Luc Vinet
Wouter van de Vijver
C1
Conference
2021
The q‐Bannai–Ito algebra and multivariate (−q)‐Racah and Bannai–Ito polynomials
Hendrik De Bie
Hadewijch De Clercq
A1
Journal Article
in
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
2021
2020
A Fock model and the Segal-Bargmann transform for the minimal representation of the orthosymplectic Lie superalgebra osp(m,2|2n)
Sigiswald Barbier
Sam Claerebout
Hendrik De Bie
A1
Journal Article
in
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
2020
A discrete realization of the higher rank Racah algebra
Hendrik De Bie
Wouter van de Vijver
A1
Journal Article
in
CONSTRUCTIVE APPROXIMATION
2020
On variational auto-encoders for fixed graph mesh learning
Nicolas Vercheval
Hendrik De Bie
Aleksandra Pizurica
C1
Conference
2020
Solutions for the Levy-Leblond or parabolic Dirac equation and its generalizations
Sijia Bao
Denis Constales
Hendrik De Bie
Teppo Mertens
A1
Journal Article
in
JOURNAL OF MATHEMATICAL PHYSICS
2020
The higher rank q-deformed Bannai-Ito and Askey-Wilson algebra
Hendrik De Bie
Hadewijch De Clercq
Wouter van de Vijver
A1
Journal Article
in
COMMUNICATIONS IN MATHEMATICAL PHYSICS
2020
Variational auto-encoders without graph coarsening for fine mesh learning
Nicolas Vercheval
Hendrik De Bie
Aleksandra Pizurica
P1
Conference
2020
2019
Bargmann and Barut-Girardello models for the Racah algebra
Hendrik De Bie
Plamen Iliev
Luc Vinet
A1
Journal Article
in
JOURNAL OF MATHEMATICAL PHYSICS
2019
2018
A higher rank Racah algebra and the Z(2)(n) Laplace–Dunkl operator
Hendrik De Bie
Vincent X Genest
Wouter van de Vijver
Luc Vinet
A1
Journal Article
in
JOURNAL OF PHYSICS A - MATHEMATICAL AND THEORETICAL
2018
A minimal representation of the orthosymplectic Lie superalgebra
Sigiswald Barbier
Hendrik De Bie
Kevin Coulembier
Dissertation
2018
Explicit formulas for the Dunkl dihedral kernel and the ( κ , a )-generalized Fourier kernel
Denis Constales
Hendrik De Bie
Pan Lian
A1
Journal Article
in
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
2018
Hypercomplex algebras for dictionary learning
Srdan Lazendic
Aleksandra Pizurica
Hendrik De Bie
C1
Conference
2018
Octonion sparse representation for color and multispectral image processing
Srdan Lazendic
Hendrik De Bie
Aleksandra Pizurica
P1
Conference
2018
On the algebra of symmetries of Laplace and Dirac operators
Hendrik De Bie
Roy Oste
Joris Van der Jeugt
A1
Journal Article
in
LETTERS IN MATHEMATICAL PHYSICS
2018
Reproducing kernels in harmonic and Clifford analysis
Michael Wutzig
Hendrik De Bie
Franciscus Sommen
Dissertation
2018
Symmetries of the S₃ Dirac-Dunkl operator
Hendrik De Bie
Roy Oste
Joris Van der Jeugt
C1
Conference
2018
The total angular momentum algebra related to the S-3 Dunkl Dirac equation
Hendrik De Bie
Roy Oste
Joris Van der Jeugt
A1
Journal Article
in
ANNALS OF PHYSICS
2018
2017
A new construction of the Clifford-Fourier kernel
Denis Constales
Hendrik De Bie
Pan Lian
A1
Journal Article
in
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
2017
A superintegrable model with reflections onSn−1and the higher rank Bannai–Ito algebra
Hendrik De Bie
Vincent X Genest
Jean-Michel Lemay
Luc Vinet
A1
Journal Article
in
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
2017
Bannai-Ito algebras and the osp(1,2) superalgebra
Hendrik De Bie
Vincent X Genest
Wouter van de Vijver
Luc Vinet
C1
Conference
2017
Basic aspects of symplectic Clifford analysis for the symplectic dirac operator
Hendrik De Bie
Marie Holíková
Petr Somberg
A1
Journal Article
in
ADVANCES IN APPLIED CLIFFORD ALGEBRAS
2017
Clifford-Fourier transform on hyperbolic space
Pan Lian
Gejun Bao
Hendrik De Bie
Denis Constales
A1
Journal Article
in
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
2017
Closed expression of the hyper-complex Fourier kernel
Pan Lian
Hendrik De Bie
Denis Constales
Gejun Bao
Dissertation
2017
Integral transforms related to the slice Dirac operator
Lander Cnudde
Hendrik De Bie
Dissertation
2017
Laplace and Dirac operators, symmetry algebras, and their use in Fourier transforms and quantum oscillator models
Roy Oste
Joris Van der Jeugt
Hendrik De Bie
Dissertation
2017
New results on the radially deformed dirac operator
Hendrik De Bie
Nele De Schepper
David Eelbode
A1
Journal Article
in
COMPLEX ANALYSIS AND OPERATOR THEORY
2017
Plane wave formulas for spherical, complex and symplectic harmonics
Hendrik De Bie
Franciscus Sommen
Michael Wutzig
A1
Journal Article
in
JOURNAL OF APPROXIMATION THEORY
2017
Slice Segal–Bargmann transform
Lander Cnudde
Hendrik De Bie
A1
Journal Article
in
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
2017
Slice fourier transform and convolutions
Lander Cnudde
Hendrik De Bie
A1
Journal Article
in
ANNALI DI MATEMATICA PURA ED APPLICATA
2017
The harmonic transvector algebra in two vector variables
Hendrik De Bie
David Eelbode
Matthias Roels
A1
Journal Article
in
JOURNAL OF ALGEBRA
2017
The higher spin Laplace operator
Hendrik De Bie
David Eelbode
Matthias Roels
A1
Journal Article
in
POTENTIAL ANALYSIS
2017
The kernel of the generalized Clifford-Fourier transform and its generating function
Pan Lian
Gejun Bao
Hendrik De Bie
Denis Constales
A1
Journal Article
in
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
2017
Transvector algebras in harmonic analysis
Matthias Roels
Hendrik De Bie
David Eelbode
Dissertation
2017
2016
A Dirac–Dunkl equation on S^2 and the Bannai–Ito algebra
Hendrik De Bie
Vincent X Genest
Luc Vinet
A1
Journal Article
in
COMMUNICATIONS IN MATHEMATICAL PHYSICS
2016
A superintegrable model with reflections on S^3 and the rank two Bannai-Ito algebra
Hendrik De Bie
Vincent X. Genest
Jean-Michel Lemay
Luc Vinet
A2
Journal Article
in
ACTA POLYTECHNICA
2016
Generalized Fourier transforms arising from the enveloping algebras of sl(2) and osp(1|2)
Hendrik De Bie
Roy Oste
Joris Van der Jeugt
A1
Journal Article
in
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
2016
Reproducing kernels for polynomial null-solutions of Dirac operators
Hendrik De Bie
Franciscus Sommen
Michael Wutzig
A1
Journal Article
in
CONSTRUCTIVE APPROXIMATION
2016
The Z(2)(n) Dirac-Dunkl operator and a higher rank Bannai-Ito algebra
Hendrik De Bie
Vincent X. Genest
Luc Vinet
A1
Journal Article
in
ADVANCES IN MATHEMATICS
2016
2015
Algebraic approach to slice monogenic functions
Lander Cnudde
Hendrik De Bie
Guangbin Ren
A1
Journal Article
in
COMPLEX ANALYSIS AND OPERATOR THEORY
2015
Conformal symmetries of the super Dirac operator
Kevin Coulembier
Hendrik De Bie
A1
Journal Article
in
REVISTA MATEMATICA IBEROAMERICANA
2015
Connecting spatial and frequency domains for the quaternion Fourier transform
Hendrik De Bie
Nele De Schepper
Todd Ell
Klaus Rubrecht
Stephen Sangwine
A1
Journal Article
in
APPLIED MATHEMATICS AND COMPUTATION
2015
Fourier transforms in Clifford analysis
Hendrik De Bie
Bookchapter
in
Operator theory
2015
Representation of distributions by harmonic and monogenic potentials in Euclidean space
Fred Brackx
Hendrik De Bie
Hennie De Schepper
A1
Journal Article
in
ADVANCES IN APPLIED CLIFFORD ALGEBRAS
2015
The Bannai-Ito algebra and some applications
Hendrik De Bie
Vincent Genest
Satoshi Tsujimoto
Luc Vinet
Alexei Zhedanov
P1
Conference
2015
Unique characterization of the Fourier transform in the framework of representation theory
Hendrik De Bie
Roy Oste
Joris Van der Jeugt
P1
Conference
2015
2014
Convolution products for hypercomplex Fourier transforms
Roxana Bujack
Hendrik De Bie
Nele De Schepper
Gerik Scheuermann
A1
Journal Article
in
JOURNAL OF MATHEMATICAL IMAGING AND VISION
2014
Generating functions of orthogonal polynomials in higher dimensions
Hendrik De Bie
Dixan Peña Peña
Franciscus Sommen
A1
Journal Article
in
JOURNAL OF APPROXIMATION THEORY
2014
Harmonic and monogenic potentials in low dimensional Euclidean half-space
Fred Brackx
Hendrik De Bie
Hennie De Schepper
A1
Journal Article
in
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
2014
On a chain of harmonic and monogenic potentials in Euclidean half-space
Fred Brackx
Hendrik De Bie
Hennie De Schepper
A1
Journal Article
in
POTENTIAL ANALYSIS
2014
The metaplectic Howe duality and polynomial solutions for the symplectic Dirac operator
Hendrik De Bie
Petr Somberg
Vladimir Souček
A1
Journal Article
in
JOURNAL OF GEOMETRY AND PHYSICS
2014
2013
Distributional boundary values of harmonic potentials in Euclidean half-space as fundamental solutions of convolution operators in Clifford analysis
Fred Brackx
Hendrik De Bie
Hennie De Schepper
Bookchapter
in
Advances in hypercomplex analysis
2013
The Clifford deformation of the Hermite semigroup
Hendrik De Bie
Bent Orsted
Petr Somberg
Vladimir Soucek
A1
Journal Article
in
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
2013
The kernel of the radially deformed Fourier transform
Hendrik De Bie
A1
Journal Article
in
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
2013
2012
Clifford algebras, Fourier transforms and quantum mechanics
Hendrik De Bie
A1
Journal Article
in
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
2012
Discrete Clifford analysis: the one-dimensional setting
Hendrik De Bie
Hilde De Ridder
Franciscus Sommen
A1
Journal Article
in
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
2012
Dunkl operators and a family of realizations of sop(1|2)
Hendrik De Bie
Bernd Orsted
Petr Somberg
Vladimir Soucek
A1
Journal Article
in
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
2012
Fractional fourier transforms of hypercomplex signals
Hendrik De Bie
Nele De Schepper
A1
Journal Article
in
SIGNAL IMAGE AND VIDEO PROCESSING
2012
New techniques for the two-sided quaternionic fourier transform
Hendrik De Bie
C1
Conference
2012
The Cauchy-Kowalewski product for bicomplex holomorphic functions
Hendrik De Bie
Daniele Struppa
Adrian Vajiac
Mihaela Vajiac
A1
Journal Article
in
MATHEMATISCHE NACHRICHTEN
2012
The fractional Clifford-Fourier transform
Hendrik De Bie
Nele De Schepper
A1
Journal Article
in
COMPLEX ANALYSIS AND OPERATOR THEORY
2012
The generating function of the Clifford-Gegenbauer polynomials
Hendrik De Bie
Dixan Peña Peña
Frank Sommen
P1
Conference
2012
Translation and convolution in Clifford analysis
Hendrik De Bie
Nele De Schepper
C1
Conference
2012
2011
Clifford-Gegenbauer polynomials related to the Dunkl Dirac operator
Hendrik De Bie
Nele De Schepper
A1
Journal Article
in
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN
2011
Fourier transforms of hypercomplex signals
Hendrik De Bie
Nele De Schepper
C1
Conference
2011
Harmonic analysis and integration in superspace
Kevin Coulembier
Hendrik De Bie
Franciscus Sommen
Dissertation
2011
Harmonic and monogenic functions in superspace
Kevin Coulembier
Hendrik De Bie
Franciscus Sommen
P1
Conference
2011
Harmonic and monogenic potentials in Euclidean half-space
Fred Brackx
Hendrik De Bie
Hennie De Schepper
C1
Conference
2011
Hilbert space for quantum mechanics on superspace
Kevin Coulembier
Hendrik De Bie
A1
Journal Article
in
JOURNAL OF MATHEMATICAL PHYSICS
2011
On the clifford-fourier transform
Hendrik De Bie
Yuan Xu
A1
Journal Article
in
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
2011
Orthogonality of Hermite polynomials in superspace and Mehler type formulae
Kevin Coulembier
Hendrik De Bie
Franciscus Sommen
A1
Journal Article
in
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
2011
The class of Clifford-Fourier transforms
Hendrik De Bie
Nele De Schepper
Franciscus Sommen
A1
Journal Article
in
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
2011
2010
Orthosymplectically invariant functions in superspace
Kevin Coulembier
Hendrik De Bie
Franciscus Sommen
A1
Journal Article
in
JOURNAL OF MATHEMATICAL PHYSICS
2010
2009
A Cauchy integral formula in superspace
Hendrik De Bie
Franciscus Sommen
A1
Journal Article
in
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
2009
An invitation to Clifford analysis on superspace
Hendrik De Bie
Franciscus Sommen
C1
Conference
2009
Integration in superspace using distribution theory
Kevin Coulembier
Hendrik De Bie
Franciscus Sommen
A1
Journal Article
in
Journal of Physics A-Mathematical and Theoretical
2009
Spherical harmonics and integration in superspace II
Hendrik De Bie
David Eelbode
Franciscus Sommen
A1
Journal Article
in
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
2009
Vector and bivector Fourier transforms in Clifford analysis
Hendrik De Bie
Franciscus Sommen
C1
Conference
2009
2008
An alternative definition of the Hermite polynomials related to the Dunkl Laplacian
Hendrik De Bie
A1
Journal Article
in
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
2008
Fischer decompositions in superspace
Hendrik De Bie
Franciscus Sommen
C1
Conference
2008
Fourier transform and related integral transforms in superspace
Hendrik De Bie
A1
Journal Article
in
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
2008
Fundamental solutions for the super Laplace and Dirac operators and all their natural powers
Hendrik De Bie
Franciscus Sommen
A1
Journal Article
in
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
2008
Harmonic and Clifford analysis in superspace
Hendrik De Bie
Franciscus Sommen
Dissertation
2008
Schrödinger equation with delta potential in superspace
Hendrik De Bie
A1
Journal Article
in
PHYSICS LETTERS A
2008
2007
A Clifford analysis approach to superspace
Hendrik De Bie
Franciscus Sommen
A1
Journal Article
in
ANNALS OF PHYSICS
2007
Correct rules for Clifford calculus on superspace
Hendrik De Bie
Franciscus Sommen
A1
Journal Article
in
ADVANCES IN APPLIED CLIFFORD ALGEBRAS
2007
Hermite and Gegenbauer polynomials in superspace using Clifford analysis
Hendrik De Bie
Franciscus Sommen
A1
Journal Article
in
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
2007
Spherical harmonics and integration in superspace
Hendrik De Bie
Franciscus Sommen
A1
Journal Article
in
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
2007