Generalized multidimensional Hilbert transforms in Clifford analysis
F Brackx, B De Knock… - International Journal of …, 2006 - Wiley Online Library
Two specific generalizations of the multidimensional Hilbert transform in Clifford analysis are
constructed. It is shown that though in each of these generalizations some traditional …
constructed. It is shown that though in each of these generalizations some traditional …
Integral Transforms of Signumdistributions
F Brackx - Complex Analysis and Operator Theory, 2024 - Springer
Expressing distributions in Euclidean space in terms of spherical coordinates gives rise to
an alternative class of continuous linear functionals, termed signumdistributions, acting on …
an alternative class of continuous linear functionals, termed signumdistributions, acting on …
The Teodorescu operator in Clifford analysis
F Brackx, H De Schepper, ME Luna-Elizarraras… - Chinese Annals of …, 2012 - Springer
Euclidean Clifford analysis is a higher dimensional function theory centred around
monogenic functions, ie, null solutions to a first order vector valued rotation invariant …
monogenic functions, ie, null solutions to a first order vector valued rotation invariant …
Two Families of Clifford Distributions Revisited
F Brackx - arXiv preprint arXiv:2402.03825, 2024 - arxiv.org
Two specific families of distributions in harmonic and Clifford analysis are further studied
through a spherical co-ordinates approach. In particular actions involving spherical co …
through a spherical co-ordinates approach. In particular actions involving spherical co …
Radial and Angular Derivatives of Distributions
F Brackx - Topics in Clifford Analysis: Special Volume in Honor of …, 2019 - Springer
When expressing a distribution in Euclidean space in spherical co-ordinates, derivation with
respect to the radial and angular co-ordinates is far from trivial. Exploring the possibilities of …
respect to the radial and angular co-ordinates is far from trivial. Exploring the possibilities of …
Distributions: a spherical co-ordinates approach
F Brackx - arXiv preprint arXiv:1801.07393, 2018 - arxiv.org
When expressing a distribution in Euclidean space in spherical co-ordinates, derivation with
respect to the radial and angular co-ordinates is far from trivial. Exploring the possibilities of …
respect to the radial and angular co-ordinates is far from trivial. Exploring the possibilities of …
On a chain of harmonic and monogenic potentials in Euclidean half–space
F Brackx, H De Bie, H De Schepper - Potential Analysis, 2014 - Springer
In the framework of Clifford analysis, a chain of harmonic and monogenic potentials is
constructed in the upper half of Euclidean space ℝ m+ 1, including a higher dimensional …
constructed in the upper half of Euclidean space ℝ m+ 1, including a higher dimensional …
Calculus for the Delta Distribution
F Brackx - Contemporary Mathematics, 2024 - ojs.wiserpub.com
A compendium of interesting identities involving the delta distribution in higher dimensional
Euclidean space is presented, ready to use as a reference work whenever modelling with …
Euclidean space is presented, ready to use as a reference work whenever modelling with …
Distributional Boundary Values of Harmonic Potentials in Euclidean Half-Space as Fundamental Solutions of Convolution Operators in Clifford Analysis
F Brackx, H De Bie, H De Schepper - Advances in Hypercomplex Analysis, 2013 - Springer
In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the
upper half of Euclidean space ℝ m+ 1 was recently constructed, including a higher …
upper half of Euclidean space ℝ m+ 1 was recently constructed, including a higher …
Higher spin dirac operators in two vector variables in Clifford analysis
L Van de Voorde - 2011 - biblio.ugent.be
The aim of this doctoral thesis is to study the construction and some properties of a speci c
higher spin Dirac operator in Cliff ord analysis. In general, a higher spin Dirac operator D is …
higher spin Dirac operator in Cliff ord analysis. In general, a higher spin Dirac operator D is …