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Changes of variables in modulation and Wiener amalgam spaces

✍ Scribed by Michael Ruzhansky; Mitsuru Sugimoto; Joachim Toft; Naohito Tomita

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 191 KB
Volume: 284
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200910199

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✦ Synopsis

In this paper various properties of global and local changes of variables as well as properties of canonical transforms are investigated on modulation and Wiener amalgam spaces. We establish several relations among localisations of such spaces and, as a consequence, we obtain several versions of local and global Beurling-Helson type theorems. We also establish 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 F L q . Finally, counterparts of these results are discussed for spaces on the torus.

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