English

Translation and modulation invariant Hilbert spaces

Functional Analysis 2020-04-07 v1

Abstract

We show that for any Hilbert space of distributions on Rd\textbf{R}^d which is translation and modulation invariant, is equal to L2(Rd)L^2(\textbf{R}^d), with the same norm apart from a multiplicative constant.

Keywords

Cite

@article{arxiv.2004.02430,
  title  = {Translation and modulation invariant Hilbert spaces},
  author = {Joachim Toft and Anupam Gumber and Ramesh Manna and P. K. Ratnakumar},
  journal= {arXiv preprint arXiv:2004.02430},
  year   = {2020}
}

Comments

6 pages

R2 v1 2026-06-23T14:40:28.567Z