H. Bie

发表

A Fock Model and the Segal-Bargmann Transform for the Minimal Representation of the Orthosymplectic Lie Superalgebra osp(m,2|2n)

S. Barbier, S. Claerebout, H. Bie, 2020, 2002.12836.

Hypercomplex algebras for dictionary learning

Aleksandra Pizurica, Srdan Lazendic, Hendrik De Bie, 2018 .

Bannai–Ito algebras and the osp(1;2) superalgebra

L. Vinet, Vincent X. Genest, W. V. D. Vijver, 2016, 1610.04797.

Implementing zonal harmonics with the Fueter principle

A. Altavilla, M. Wutzig, H. Bie, 2019, Journal of Mathematical Analysis and Applications.

Representations of the Lie Superalgebra osp(1|2n) with Polynomial Bases

J. V. Jeugt, H. Bie, A. K. Bisbo, 2019, Symmetry, Integrability and Geometry: Methods and Applications.

The Racah algebra: An overview and recent results

L. Vinet, P. Iliev, H. D. Bie, 2020, 2001.11195.

The total angular momentum algebra related to the S3 Dunkl Dirac equation

J. V. Jeugt, H. D. Bie, R. Oste, 2017, 1705.08751.

The harmonic transvector algebra in two vector variables

D. Eelbode, H. Bie, Matthias Roels, 2015, 1510.06566.

Orthosymplectically invariant functions in superspace

F. Sommen, K. Coulembier, H. Bie, 2010, 1006.4744.

A Discrete Realization of the Higher Rank Racah Algebra

W. V. D. Vijver, H. Bie, 2018, Constructive Approximation.

Correct Rules for Clifford Calculus on Superspace

F. Sommen, H. Bie, 2007 .

On the Clifford-Fourier transform

H. De Bie, Y. Xu, Y. Xu, 2010, 1003.0689.

A Clifford analysis approach to superspace

F. Sommen, H. Bie, 2007, 0707.2859.

The kernel of the radially deformed Fourier transform

H. Bie, 2013, 1303.2979.

The Clifford Deformation of the Hermite Semigroup

V. Souček, H. D. Bie, B. Orsted, 2011, 1101.5551.

The Fractional Clifford-Fourier Transform

N. D. Schepper, H. D. Bie, H. Bie, 2012, 1209.5955.

Generalized Fourier Transforms Arising from the Enveloping Algebras of (2) and (1∣2)

J. V. Jeugt, H. D. Bie, R. Oste, 2014, 1411.6856.

C A ] 2 J ul 2 01 5 Generalized Fourier transforms arising from the enveloping algebras of sl ( 2 ) and osp ( 1 | 2 )

J. V. Jeugt, H. D. Bie, R. Oste, 2018 .

The Class of Clifford-Fourier Transforms

H. De Bie, F. Sommen, N. De Schepper, 2011, 1101.1793.

Superspace realizations of the Bannai–Ito algebra

L. Vinet, P. Iliev, N. Crampé, 2023, Letters in Mathematical Physics.

The q‐Bannai–Ito algebra and multivariate (−q)‐Racah and Bannai–Ito polynomials

H. Bie, Hadewijch De Clercq, 2019, 1902.07883.

The Z(2)(n) Dirac-Dunkl operator and a higher rank Bannai-Ito algebra

L. Vinet, Vincent X. Genest, H. Bie, 2016 .

The $\mathbb{Z}_2^n$ Dirac-Dunkl operator and a higher rank Bannai-Ito algebra

L. Vinet, Vincent X. Genest, H. Bie, 2015, 1511.02177.

An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian

H. Bie, 2008, 0812.4819.

Fourier transform and related integral transforms in superspace

H. De Bie, H. Bie, 2008, 0805.1918.

Generating functions of orthogonal polynomials in higher dimensions

Dixan Peña Peña, Frank Sommen, Hendrik De Bie, 2013, J. Approx. Theory.

Octonion Sparse Representation for Color and Multispectral Image Processing

Aleksandra Pizurica, Srdan Lazendic, Hendrik De Bie, 2018, 2018 26th European Signal Processing Conference (EUSIPCO).

Clifford algebras, Fourier transforms and quantum mechanics

Hendrik De Bie, H. D. Bie, H. Bie, 2012, 1209.6434.

The Clifford-Helmholtz system and related Fourier transforms Het

R. Oste, Toelating tot bruikleen, H. Bie, 2013 .

The Higher Spin Laplace Operator

D. Eelbode, H. Bie, Matthias Roels, 2015, 1501.03974.

Polynomial Representations of the Lie Superalgebra osp(1|2n)

H. Bie, A. K. Bisbo, J. Jeugt, 2019, 1912.06488.

Harmonic and Monogenic Functions in Superspace

F. Sommen, K. Coulembier, H. Bie, 2011 .

Generalized Fourier transforms and unique characterization of the Fourier transform

R. Oste, H. Bie, J. Jeugt, 2014 .

Distributional Boundary Values of Harmonic Potentials in Euclidean Half-Space as Fundamental Solutions of Convolution Operators in Clifford Analysis

F. Brackx, H. Schepper, H. Bie, 2012, 1210.2389.

On a Chain of Harmonic and Monogenic Potentials in Euclidean Half–space

F. Brackx, H. Schepper, H. Bie, 2012, 1210.2044.

Dunkl operators and a family of realizations of osp(1|2)

V. Souček, P. Somberg, H. Bie, 2009, 0911.4725.

Fundamental solutions for the super Laplace and Dirac operators and all their natural powers

F. Sommen, H. D. Bie, H. Bie, 2007, 0707.2862.

Hilbert space for quantum mechanics on superspace

K. Coulembier, H. Bie, 2011, 1101.4820.

Convolution Products for Hypercomplex Fourier Transforms

Gerik Scheuermann, Roxana Bujack, Nele De Schepper, 2013, Journal of Mathematical Imaging and Vision.

Dunkl operators and Clifford algebras

H. Bie, 2011 .

The Dunkl kernel and intertwining operator for dihedral groups

P. Lian, H. Bie, 2020, Journal of Functional Analysis.

Symmetries of the $S_3$ Dirac–Dunkl Operator

R. Oste, H. Bie, J. Jeugt, 2017 .

Explicit formulas for the Dunkl dihedral kernel and the $(\kappa, a)$-generalized Fourier kernel

D. Constales, P. Lian, H. Bie, 2016, 1610.00098.

Connecting spatial and frequency domains for the quaternion Fourier transform

Stephen J. Sangwine, Todd A. Ell, Nele De Schepper, 2015, Appl. Math. Comput..

Schrödinger equation with delta potential in superspace

H. Bie, 2008, 0805.1933.

Fourier transforms in Clifford analysis

H. D. Bie, H. Bie, 2015 .

Explicit formulas for the Dunkl dihedral kernel and the ( κ, a )-generalized Fourier kernel

D. Constales, P. Lian, H. Bie, 2017 .