Hilbert spaces of tempered distributions, Hermite expansions and sequence spaces

DOI10.1017/S0013091500007173zbMath0788.46042OpenAlexW2087512137MaRDI QIDQ3991572

Rainer Picard

Publication date: 28 June 1992

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0013091500007173

zbMATH Keywords

characterization of tempered distributions by covergent Hermite expansionsHilbert space approach to distributionsorthonormal expansions in Hilbert spacescale of Sobolev type Hilbert spaces

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Topological linear spaces of test functions, distributions and ultradistributions (46F05)

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Cites Work

• A Hilbert space approach to distributions
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