Isomorphism properties of Toeplitz operators and pseudo-differential operators between modulation spaces

2009/05/29 by Karlheinz Gröchenig, Karl-Heinz Gröchenig, Gröchenig, Karl-Heinz +2 · 2 citations
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #math.FA

paper · pdf · doi:10.48550/arxiv.0905.4954

27 pages

openalex publication_date 2009/05/29 · arxiv created 2009/10/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

We investigate the lifting property of modulation spaces and construct explicit isomorpisms between them. For each weight function ω and suitable window function \fy , the Toeplitz operator (or localization operator) \tp_\fy (ω) is an isomorphism from M^p,q_(ω0) onto M^p,q_(ω0/ω) for every p,q ∈ [1,∞ ] and arbitrary weight function ω₀. The methods involve the pseudo-differential calculus of Bony and Chemin and the Wiener algebra property of certain symbol classes of pseudo-differential operators.

Cited by

• The Lifting Property for Frame Multipliers and Toeplitz Operators
• Weighted symbol spaces, magnetic translations, and pseudodifferential operators
• Filtering of second order generalized stochastic processes corrupted by additive noise

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