Fourier multipliers and pseudo-differential operators on Fock-Sobolev spaces

2023/04/03 by Sundaram Thangavelu, Thangavelu, Sundaram
Mathematics · #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2304.01087

openalex publication_date 2023/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Any bounded linear operator T on L²(ℝⁿ) gives rise to the operator S= B ∘ T ∘ B^∗ on the Fock space F(\Cⁿ) where B is the Bargmann transform. In this article we identify those S which correspond to Fourier multipliers and pseudo-differential operators on L²(ℝⁿ) and study their boundedness on the Fock-Sobolev spaces F^s,2(\Cⁿ).

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