Non-isometric translation and modulation invariant Hilbert spaces
Let H be a Hilbert space, continuously embedded in S'(Rd), and which contains at least one non-zero element in S'(Rd). If there is a constant C0 > 0 such that ||ei❮· ,ε❯ f ( · -x)||H ≤ C0||f||H, f ∈ H, x, ε ∈ Rd, then we prove that H = L2(Rd), with equivalent norms.
Authors
- Joachim Toft (ORCID: https://orcid.org/0000-0003-1921-8168)
- P. K. Ratnakumar
- Jasson Vindas (ORCID: https://orcid.org/0000-0002-3789-8577)
Publication Details
- Journal
- Journal of Mathematical Analysis and Applications
- Published
- 2025-03-29
- DOI
- https://doi.org/10.1016/j.jmaa.2025.129530
- Primary Topic
- Mathematical Analysis and Transform Methods
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Fonds Wetenschappelijk Onderzoek
- Vetenskapsrådet
- Vlaamse regering