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

By Karlheinz Gröchenig, J. Toft. 2009

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We investigate the lifting property of modulation spaces and construct explicit isomorphisms between them. For each weight function ω and suitable window function φ, the Toeplitz operator (or localization operator) Tpφ(ω) is an isomorphism from $$M_{({\omega _0})}^{p,q}$$, onto $$M_{({\omega _0}/\omega )}^{p,q}$$ 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.

Subfields: Applied Mathematics, Mathematical Physics

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