Eigenfunction expansions for generalized functions of several variables

W. Lamb, D.F. McGhee

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)239-249
Number of pages10
JournalIntegral Transforms and Special Functions
Issue number3
Publication statusPublished - Jun 2004


  • generalized functions
  • eigenfunction expansions
  • spherical harmonics

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