The Zak transform and Wiener estimates on Gelfand-Shilov and modulation\n spaces with applications to operator theory

2017/05/28 by Joachim Toft, Toft, Joachim
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1705.10619

openalex publication_date 2017/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize Gelfand-Shilov spaces, their distribution spaces and\nmodulation spaces in terms of estimates of their Zak transforms. We use these\nresult for general investigations of quasi-periodic functions and\ndistributions. We also establish necessary and sufficient conditions for linear\noperators in order for these operators should be conjugations by the Zak\ntransform.\n

Citations

• Semi-continuous convolutions on weakly periodic Lebesgue spaces

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