A Beurling-Helson type theorem for modulation spaces - Kasso A. Okoudjou (Journal of Function Spaces and Applications)
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 ℳp,q(ℝd) are affine functions on ℝd. A special case of our result involving the Sjöstrand algebra was considered earlier by A. Boulkhemair.