Images of function and distribution spaces under the Bargmann transform

2014/09/18 by Joachim Toft, Toft, Joachim · 2 citations
Mathematics · #30Gxx (Secondary) #33C10 #35Q40 #35S05 #46F05 (Primary) #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1409.5238

openalex publication_date 2014/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a broad family of test function spaces and their dual (distribution) space. The family includes Gelfand-Shilov spaces, a family of test function spaces introduced by S. Pilipovic. We deduce different characterizations of such spaces, especially under the Bargmann transform and the Short-time Fourier transform. The family also include a test function space, whose dual space is mapped by the Bargmann transform bijectively to the set of entire functions.

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• Quantitative uncertainty principles for time-frequency Gaussian decay
• Sparse Gabor representations of metaplectic operators: controlled exponential decay and Schrödinger confinement

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