Changes of variables in modulation and Wiener amalgam spaces. (English) Zbl 1228.35279
The authors study various properties of global and local changes of variables as well as properties of canonical transforms on modulation and Wiener amalgam spaces. There are established several relations among localisations of such spaces and, as a consequence, there are obtained several versions of local and global Beurling-Helson type theorems. A number of positive results such as local boundedness of canonical transforms on modulation spaces, properties of homogeneous changes of variables, and local continuity of Fourier integral operators on \(FL^q\) are also established. Finally, counterparts of these results are discussed for spaces on the torus.
Reviewer: Lubomira Softova (Aversa)
MSC:
| 35S30 | Fourier integral operators applied to PDEs |
| 47G30 | Pseudodifferential operators |
| 42B05 | Fourier series and coefficients in several variables |
Keywords:
modulation spaces; Wiener amalgam spaces; Wiener type spaces; changes of variables; Beurling-Helson’s theorem; Fourier integral operators; function spaces on torusReferences:
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