Complete orthogonal Appell systems for spherical monogenics
R Lávička - Complex Analysis and Operator Theory, 2012 - Springer
In this paper, we investigate properties of Gelfand–Tsetlin bases mainly for spherical
monogenics, that is, for spinor valued or Clifford algebra valued homogeneous solutions of …
monogenics, that is, for spinor valued or Clifford algebra valued homogeneous solutions of …
Canonical bases for sl (2, C)-modules of spherical monogenics in dimension 3
R Lavicka - arXiv preprint arXiv:1003.5587, 2010 - arxiv.org
Spaces of homogeneous spherical monogenics in dimension 3 can be considered naturally
as sl (2, C)-modules. As finite-dimensional irreducible sl (2, C)-modules, they have …
as sl (2, C)-modules. As finite-dimensional irreducible sl (2, C)-modules, they have …
The Cauchy–Kovalevskaya extension theorem in Hermitian Clifford analysis
F Brackx, H De Schepper, R Lávička… - Journal of mathematical …, 2011 - Elsevier
Hermitian Clifford analysis is a higher dimensional function theory centered around the
simultaneous null solutions, called Hermitian monogenic functions, of two Hermitian …
simultaneous null solutions, called Hermitian monogenic functions, of two Hermitian …
On orthogonal monogenics in oblate spheroidal domains and recurrence formulae
HM Nguyen, K Gürlebeck, J Morais… - Integral Transforms and …, 2014 - Taylor & Francis
A complete orthogonal system for the monogenic L 2-space consisting of solid oblate
spheroidal monogenics in 3 is constructed by means of harmonic functions. The lack of …
spheroidal monogenics in 3 is constructed by means of harmonic functions. The lack of …
Introductory clifford analysis
H De Schepper, F Sommen - Operator theory, 2015 - biblio.ugent.be
In this chapter an introduction is given to Clifford analysis and the underlying Clifford
algebras. The functions under consideration are defined on Euclidean space and take …
algebras. The functions under consideration are defined on Euclidean space and take …
Orthogonalization in Clifford Hilbert modules and applications
J Wang, T Qian - Banach Journal of Mathematical Analysis, 2024 - Springer
We prove that the Gram–Schmidt orthogonalization process can be carried out in Hilbert
modules over Clifford algebras, in spite of the un-invertibility and the un-commutativity of …
modules over Clifford algebras, in spite of the un-invertibility and the un-commutativity of …
Orthogonal Appell bases for Hodge-de Rham systems in Euclidean spaces
R Lávička - Advances in Applied Clifford Algebras, 2013 - Springer
Abstract Recently the Gelfand-Tsetlin construction of orthogonal bases has been explicitly
described for homogeneous polynomial solutions of the Hodge-de Rham systems in the …
described for homogeneous polynomial solutions of the Hodge-de Rham systems in the …
Generalized Appell property for the Riesz system in dimension 3
R Lávička - … Conference on Numerical Analysis and Applied …, 2011 - ui.adsabs.harvard.edu
In this note, we give an explicit description of orthogonal (even the Gelfand-Tsetlin) bases for
the spaces of homogeneous solutions of the Riesz system in R 3 using hypergeometric …
the spaces of homogeneous solutions of the Riesz system in R 3 using hypergeometric …
Generating functions for spherical harmonics and spherical monogenics
In this paper, we study generating functions for the standard orthogonal bases of spherical
harmonics and spherical monogenics in R^ m R m. Here spherical monogenics are …
harmonics and spherical monogenics in R^ m R m. Here spherical monogenics are …
Hermitian clifford analysis
I Sabadini, F Sommen - Operator theory, 2015 - biblio.ugent.be
This paper gives an overview of some basic results on Hermitian Clifford analysis, a
refinement of classical Clifford analysis dealing with functions in the kernel of two mutually …
refinement of classical Clifford analysis dealing with functions in the kernel of two mutually …