Joachim Toft

Continuity and Schatten Properties for Pseudo-differential Operators on Modulation Spaces

Let M (ω) p,q be the modulation space with parameters p, q and weight function ω. We prove that if t ∈ R, p, p j, q, q j ∈ [1, ∞], ω 1, ω 2 and ω are appropriate, and a ∈ M (ω) p,q , then the pseudo-differential operator a t(x,D) is continuous from M (ω) p1,q1 to M (ω) p2,q2 . If in addition p j = q j = 2, then we establish necessary and sufficient conditions on p and q in order to a t(x,D) should be a Schatten-von Neumann operator of certain order.

Schatten–von Neumann properties for Fourier integral operators with non-smooth symbols, I

We consider Fourier integral operators with symbols in modulation spaces and non-smooth phase functions whose second orders of derivatives belong to certain types of modulation space. We establish continuity and Schatten-von Neumann properties of such operators when acting on modulation spaces.

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

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

Embeddings and compactness for generalized Sobolev–Shubin spaces and modulation spaces

M_{({\omega _0})}^{p,q}

Continuity and Schatten Properties for Toeplitz Operators on Modulation Spaces

, onto

Gabor Analysis for a Broad Class of Quasi-Banach Modulation Spaces

M_{({\omega _0}/\omega )}^{p,q}