Changes of variables in modulation and Wiener amalgam spaces
Changes of variables in modulation and Wiener amalgam spaces
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DOI：
10.1002/mana.200910199
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发表时间：
2008-03
影响因子：
1
通讯作者：
Michael Ruzhansky;M. Sugimoto;J. Toft;Naohito Tomita
中科院分区：
文献类型：
--
作者：
Michael Ruzhansky;M. Sugimoto;J. Toft;Naohito Tomita
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 \documentclass{article}\usepackage{amssymb, mathrsfs}\begin{document}\pagestyle{empty}${\mathscr F}L^q$\end{document}. Finally, counterparts of these results are discussed for spaces on the torus.
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 \documentclass{article}\usepackage{amssymb, mathrsfs}\begin{document}\pagestyle{empty}${\mathscr F}L^q$\end{document}. Finally, counterparts of these results are discussed for spaces on the torus.