Composition and Spectral Invariance of Pseudodifferential Operators on Modulation Spaces

Spectral Invariance for Pseudodifferential Operators on Function Spaces

Pseudodifferential Operators on L, Wiener Amalgam and Modulation Spaces

We give a complete characterization of the continuity of pseudodifferential operators with symbols in modulation spaces M, acting on a given Lebesgue space L. Namely, we find the full range of triples (p, q, r), for which such a boundedness occurs. More generally, we completely characterize the same problem for operators acting on Wiener amalgam space W (L, L) and even on modulation spaces M . ...

Multilinear Localization Operators

In this paper we introduce a notion of multilinear localization operators. By reinterpreting these operators as multilinear Kohn-Nirenberg pseudodifferential operators, we prove that these multilinear localization operators are bounded on products of modulation spaces. In particular, by assuming that the symbols of the localization operators belong to the largest modulation space, i.e., M , we ...

Modulation Spaces as Symbol Classes for Pseudodifferential Operators

We investigate the Weyl calculus of pseudodifferential operators with the methods of time-frequency analysis. As symbol classes we use the modulation spaces, which are the function spaces associated to the short-time Fourier transform and the Wigner distribution. We investigate the boundedness and Schatten-class properties of pseudodifferential operators, and furthermore we study their mapping ...

Families Index for Pseudodifferential Operators on Manifolds with Boundary

An analytic families index is defined for (cusp) pseudodifferential operators on a fibration with fibres which are compact manifolds with boundaries. This provides an extension to the boundary case of the setting of the (pseudodifferential) Atiyah-Singer theorem and to the pseudodifferential case of the families Atiyah-Patodi-Singer index theorem for Dirac operators due to Bismut and Cheeger an...