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Journal of Function Spaces and Applications
Volume 7, Issue 1, Pages 33-41

A Beurling-Helson type theorem for modulation spaces

Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

Received 1 January 2008

Academic Editor: Hans Feightinger

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We prove a Beurling-Helson type theorem on modulation spaces. More precisely, we show that the only 𝒞1 changes of variables that leave invariant the modulation spaces p,q(ℝd) are affine functions on ℝd. A special case of our result involving the Sjöstrand algebra was considered earlier by A. Boulkhemair.