Kasso A Okoudjou

A Beurling-Helson type theorem for modulation spaces

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