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The Gelfand-Tsetlin bases for Hodge-de Rham systems in Euclidean spaces
even theso-called Gelfand-Tsetlin bases for such spaces in terms of Gegenbauer polynomials. As an application, we obtain an algorithm how to compute an orthogonal basis......
BA - Obecná matematika
- 2012 •
- Jx •
- Link
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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Orthogonal Appell Bases for Hodge-de Rham Systems in Euclidean Spaces
Recently the Gelfand-Tsetlin construction of orthogonal bases has been explicitly described for homogeneous polynomial solutions of the Hodge-de Rham systems in the Euclidean space of any dimension. In this paper, we study propertie...
BA - Obecná matematika
- 2013 •
- Jx •
- Link
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Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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The Gelfand-Tsetlin bases for spherical monogenics in dimension 3
The main aim of this paper is to recall the notion of the Gelfand-Tsetlin bases (GT bases for short) and to use it for an explicit construction of orthogonal bases for the spaces of spherical monogenics (i.e., homogeneous solutions ...
BA - Obecná matematika
- 2012 •
- Jx •
- Link
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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Gelfand-Tsetlin Bases of Orthogonal Polynomials in Hermitean Clifford Analysis
An explicit algorithmic construction is given for orthogonal bases for spaces of homogeneous polynomials, in the context of Hermitean Clifford analysis, which is a higher dimensional function theory centered around the simultaneous null solutions of ...
BA - Obecná matematika
- 2011 •
- Jx •
- Link
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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Complete Orthogonal Appell Systems for Spherical Monogenics
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 the Dirac equation in the Euclidean space. Recently it...
BA - Obecná matematika
- 2012 •
- Jx •
- Link
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Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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Generalized Appell Property for the Riesz System in Dimension 3
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 dimension 3 using hypergeometric series. Moreover, we show that the basi...
BA - Obecná matematika
- 2011 •
- D •
- Link
Rok uplatnění
D - Stať ve sborníku
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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. Here spherical monogenics are polynomial solutions of the Dirac equation. In particular, we obtain the recurrence formula ...
BA - Obecná matematika
- 2014 •
- Jx •
- Link
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Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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Fischer Decompositions of Kernels of Hermitean Dirac Operators
In this note we describe explicitly irreducible decompositions of kernels of the Hermitean Dirac Operators. It turns out that these decompositions are essential for a construction of orthogonal (or even Gelfand-Tsetlin) bases of hom...
BA - Obecná matematika
- 2010 •
- D
Rok uplatnění
D - Stať ve sborníku
Gel'fand-Tsetlin procedure for the construction of orthogonal bases in Hermitean Cli fford analysis
In this note, we describe the Gel'fand-Tsetlin construction of an orthogonal basis in spaces of Hermitean monogenic polynomials.
BA - Obecná matematika
- 2010 •
- D
Rok uplatnění
D - Stať ve sborníku
q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra U-q(u(n, 1))
(n + 1)), namely, an orthonormal Gelfand-Graev basis is constructed...
BA - Obecná matematika
- 2010 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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