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On the Completeness and Closure of Vector and Tensor Spherical Harmonics

  • An intrinsically on the 2-sphere formulated proof of the closure and completeness of spherical harmonics is given in vectorial and tensorial framework. The considerations are essentially based on vector and tensor approximation in terms of zonal vector and tensor Bernstein kernels, respectively.
  • Ein Beweis der Vollständigkeit und Abgeschlossenheit der Kugelflächenfunktionen, der intrinsisch auf der 2-Sphäre formuliert ist, wird im vektoriellen wie im tensoriellen Rahmen dargestellt. Die Betrachtungen basieren essentiell auf vektorieller und tensorieller Approximation mittels zonalen vektoriellen beziehungsweise tensoriellen Bernstein Kernen.

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Metadaten
Author:Willi Freeden, Martin Gutting
URN:urn:nbn:de:hbz:386-kluedo-15199
Series (Serial Number):Schriften zur Funktionalanalysis und Geomathematik (37)
Document Type:Preprint
Language of publication:English
Year of Completion:2008
Year of first Publication:2008
Publishing Institution:Technische Universität Kaiserslautern
Date of the Publication (Server):2008/04/07
Tag:Abgeschlossenheit; Bernstein Kern
GND Keyword:Vollständigkeit; Orthonormalbasis; Vektorfeld; Tensorfeld; Kugelflächenfunktion; Sphäre
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):30-XX FUNCTIONS OF A COMPLEX VARIABLE (For analysis on manifolds, see 58-XX) / 30Fxx Riemann surfaces / 30F15 Harmonic functions on Riemann surfaces
33-XX SPECIAL FUNCTIONS (33-XX DEALS WITH THE PROPERTIES OF FUNCTIONS AS FUNCTIONS) (For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for representation theory see 22Exx) / 33Cxx Hypergeometric functions / 33C55 Spherical harmonics
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Pxx Spectral theory and eigenvalue problems [See also 47Axx, 47Bxx, 47F05] / 35P10 Completeness of eigenfunctions, eigenfunction expansions
42-XX FOURIER ANALYSIS / 42Cxx Nontrigonometric harmonic analysis / 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
42-XX FOURIER ANALYSIS / 42Cxx Nontrigonometric harmonic analysis / 42C30 Completeness of sets of functions
43-XX ABSTRACT HARMONIC ANALYSIS (For other analysis on topological and Lie groups, see 22Exx) / 43Axx Abstract harmonic analysis / 43A90 Spherical functions [See also 22E45, 22E46, 33C55]
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011