A remark on the Weyl quantisation of Paley-Wiener functions

2025/02/19 by Helge J. Samuelsen, Samuelsen, Helge J.
Mathematics · #42B10 #47B10 #47G30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2502.13798

openalex publication_date 2025/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a short proof of the fact that the Weyl quantisation of a tempered distribution with compactly supported Fourier transform is in the Schatten p-class if and only if the symbol is L^p-integrable. The proof is based on Werner-Young's inequality from quantum harmonic analysis and a quantum version of Wiener's division lemma.

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