2025/02/11 by Nikolas Hauschka, Hauschka, Nikolas, Péter Balázs +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Cosmology and Gravitation Theories #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2502.07378
openalex publication_date 2025/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Associated with every separable Hilbert space H and a given localized frame, there exists a natural test function Banach space H1 and a Banach distribution space H∞ so that H1 ⊂ H ⊂ H∞. In this article we close some gaps in the literature and rigorously introduce the space H∞ and its weighted variants Hw∞ in a slightly more general setting and discuss some of their properties. In particular, we compare the underlying weak^*- with the norm topology associated with Hw∞ and show that (Hw∞, \Vert ⋅ \VertHw∞) is a Banach space.