Changes of variables in modulation and Wiener amalgam spaces

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Title: Changes of variables in modulation and Wiener amalgam spaces
Authors: Ruzhansky, M
Sugimoto, M
Toft, J
Tomita, N
Item Type: Journal Article
Abstract: 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 equation image. Finally, counterparts of these results are discussed for spaces on the torus.
Issue Date: 6-Oct-2011
Date of Acceptance: 29-Mar-2010
URI: http://hdl.handle.net/10044/1/55318
DOI: https://dx.doi.org/10.1002/mana.200910199
ISSN: 0025-584X
Publisher: Wiley-VCH Verlag
Start Page: 2078
End Page: 2092
Journal / Book Title: Mathematical News / Mathematische Nachrichten
Volume: 284
Issue: 16
Copyright Statement: This is the peer reviewed version of the following article: Ruzhansky, M., Sugimoto, M., Toft, J. and Tomita, N. (2011), Changes of variables in modulation and Wiener amalgam spaces. Math. Nachr., 284: 2078–2092, which has been published in final form at https://dx.doi.org/10.1002/mana.200910199.  This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/G007233/1
Keywords: Science & Technology
Physical Sciences
Mathematics
Modulation spaces
Wiener amalgam spaces
Wiener type spaces
changes of variables
Beurling-Helson's theorem
Fourier integral operators
function spaces on torus
FOURIER INTEGRAL-OPERATORS
ATOMIC DECOMPOSITIONS
GROUP-REPRESENTATIONS
MULTIPLIERS
EQUATIONS
PROPERTY
math.FA
math.AP
35S30, 47G30, 42B05
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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