Holomorphic Sobolev spaces, Hermite ans special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

2007/10/18 by R. Radha, S. Thangavelu, Sundaram Thangavelu +2
Mathematics · #42 B 35 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #math.FA #msc:35 #msc:42

paper · pdf · doi:10.48550/arxiv.0710.3481

17 pages

arxiv created 2007/10/18 · openalex publication_date 2007/10/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The images of Hermite and Laguerre Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterised. These are used to characterise the Schwartz class of rapidly decreasing functions. The image of the space of all tempered distributions is also considered and a Paley-Wiener theorem for the windowed Fourier transform is proved.

Citations

• Holomorphic Sobolev spaces and the generalized Segal–Bargmann transform

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