A Beurling-Helson type theorem for modulation spaces. Issue 1 (2009)

• Record Type: Journal Article
• Authors: Okoudjou Okoudjou, Kasso A. Kasso A.
• Other Names: Feightinger Feightinger Hans Hans Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 7:Issue 1(2009)
• Page Start: 33
• Page End: 41
• Publication Date: 2009
• Subjects: Beurling-Helson theorem, changes of variables, Feichtinger algebra, Fourier multipliers, modulation spaces, Sjöstrand algebra.; Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2009/956891
• Languages: English
• ISSNs: 0972-6802

Abstract

Abstract : We prove a Beurling-Helson type theorem on modulation spaces. More precisely, we show that the only 𝒞 1 changes of variables that leave invariant the modulation spaces ℳ p, q (ℝ d ) are affine functions on ℝ d . A special case of our result involving the Sjöstrand algebra was considered earlier by A. Boulkhemair.