Non-isometric translation and modulation invariant Hilbert spaces

P. K. Ratnakumar, Joachim Toft, Jasson Vindas

Let $\mathcal{H}$ be a Hilbert space of distributions on ${\mathbf{R}}^d$ which contains at least one non-zero element in ${\mathcal{D}}^{\prime }({\mathbf{R}}^d)$. If there is a constant $C_0>0$ su…