The Bargmann transform on a broad family of Banach spaces, with applications to Toeplitz and pseudo-differential operators

2011/02/02 by Joachim Toft, Toft, Joachim · 1 citation
Mathematics · #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #math.AP #math.CV #math.FA

paper · pdf · doi:10.48550/arxiv.1102.0336

openalex publication_date 2011/02/02 · arxiv created 2011/06/22 · arxiv updated 2011/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate mapping properties for the Bargmann transform on modulation spaces whose weights and their reciprocals are allowed to grow faster than exponentials. We prove that this transform is isometric and bijective from modulation spaces to convenient Lebesgue spaces of analytic functions. We use this to prove that such modulation spaces fulfill most of the continuity properties which are well-known when the weights are moderated. Finally we use the results to establish continuity properties of Toeplitz and pseudo-differential operators in the context of these modulation spaces.

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