Work

The range of localization operators and lifting theorems for modulation and Bargmann-Fock spaces

Year: 2013

Type: article

Abstract: We study the range of time-frequency localization operators acting on modulation spaces and prove a lifting theorem. As an application we also characterize the range of Gabor multipliers, and, in the realm of complex analysis, we characterize the range of certain Toeplitz operators on weighted Bargmann-Fock spaces. The main tools are the construction of canonical isomorphisms between modulation spaces of Hilbert-type and a refined version of the spectral invariance of pseudodifferential operators. On the technical level we prove a new class of inequalities for weighted gamma functions.

Source: Transactions of the American Mathematical Society

DOI: 10.1090/s0002-9947-2013-05836-9

Authors: Karlheinz Gröchenig, Joachim Toft

Institutions: University of Vienna, Linnaeus University

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Austrian Science Fund

OpenAlex ID: W1991574347