Eigenfunction expansions for generalized functions of several variables

W. Lamb, D.F. McGhee

Research output: Contribution to journalArticle

Abstract

The constructive method developed by Zemanian [Zemanian, A. H. (1968). Generalized Integral Transformations. Interscience, New York] for extending L2-convergence results on eigenfunction expansions to certain classes of generalized functions of one variable is shown to be valid also for generalized functions of several variables. In the latter case, the expansions involve the eigenfunctions associated with symmetric partial differential operators. Specific examples considered are the Laplace-Beltrami operator on the unit sphere in ℝN and a class of symmetric elliptic operators in L2(Φ#169;), where Φ#169; is a bounded region in ℝN. Applications to the solution of distributional initial-boundary value problems are also discussed.
LanguageEnglish
Pages239-249
Number of pages10
JournalIntegral Transforms and Special Functions
Volume15
Issue number3
DOIs
Publication statusPublished - Jun 2004

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Eigenfunction Expansion
Several Variables
Generalized Functions
Eigenvalues and eigenfunctions
Integral Transformation
Laplace-Beltrami Operator
Symmetric Operator
Partial Differential Operators
Unit Sphere
Elliptic Operator
Convergence Results
Initial-boundary-value Problem
Boundary value problems
Eigenfunctions
Valid
Class

Keywords

  • generalized functions
  • eigenfunction expansions
  • spherical harmonics

Cite this

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Eigenfunction expansions for generalized functions of several variables. / Lamb, W.; McGhee, D.F.

In: Integral Transforms and Special Functions, Vol. 15, No. 3, 06.2004, p. 239-249.

Research output: Contribution to journalArticle

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AU - McGhee, D.F.

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