Work

Non-isometric translation and modulation invariant Hilbert spaces

Year: 2025

Type: article

Abstract: Let H be a Hilbert space , continuously embedded in S ′ ( R d ) , and which contains at least one non-zero element in S ′ ( R d ) . If there is a constant C 0 > 0 such that ‖ e i 〈 ⋅ , ξ 〉 f ( ⋅ − x ) ‖ H ≤ C 0 ‖ f ‖ H , f ∈ H , x , ξ ∈ R d , then we prove that H = L 2 ( R d ) , with equivalent norms.

Source: Journal of Mathematical Analysis and Applications

DOI: 10.1016/j.jmaa.2025.129530

Authors: P.K. Ratnakumar, Joachim Toft, Jasson Vindas

Institutions: Harish-Chandra Research Institute, Linnaeus University, Ghent University

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190