Non-isometric translation and modulation invariant Hilbert spaces

2024/07/11 by P. K. Ratnakumar, Ratnakumar, P. K., Joachim Toft +2 · 1 citation
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2407.08435

openalex publication_date 2024/07/11 · openalex created_date 2024/07/14 · openalex updated_date 2026/07/28

Abstract

Let \mathcal H be a Hilbert space of distributions on \mathbf R^d which contains at least one non-zero element in \mathscr D '(\mathbf R^d). If there is a constant C₀>0 such that \nm e^{i\scal \cdo ξ}f(\cdo -x)\mathcal H≤ C₀\nm f\mathcal H, f∈ \mathcal H , x,ξ∈ \mathbf R^d, then we prove that \maclH = L²(\mathbf R^d), with equivalent norms.

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