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arXiv · 2004.02430

Translation and modulation invariant Hilbert spaces

Joachim Toft·Anupam Gumber·Ramesh Manna·P. K. Ratnakumar
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Abstract

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

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Joachim Toft, Anupam Gumber, Ramesh Manna, P. K. Ratnakumar. 2020-04-06. Translation and modulation invariant Hilbert spaces. https://arxiv.org/abs/2004.02430

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