In this note we present a review, some considerations and new results about maps with values in a distribution space and domain in a σ-finite measure space X. Namely, this is a survey about Bessel maps, frames and bases (in particular Riesz and Gel’fand bases) in a distribution space. In this setting, the Riesz-Fischer maps and semi-frames are defined and new results about them are obtained. Some examples in tempered distributions space are examined.
Francesco Tschinke (2020). Riesz-Fischer maps, semi-frames and frames in rigged Hilbert spaces. In M.A. Bastos, L. Castro, & A.Y. Karlovich (a cura di), Operator Theory, Functional Analysis and Applications (pp. 1-18). Birkhäuser.
Data di pubblicazione: | 2020 |
Titolo: | Riesz-Fischer maps, semi-frames and frames in rigged Hilbert spaces |
Autori: | |
Citazione: | Francesco Tschinke (2020). Riesz-Fischer maps, semi-frames and frames in rigged Hilbert spaces. In M.A. Bastos, L. Castro, & A.Y. Karlovich (a cura di), Operator Theory, Functional Analysis and Applications (pp. 1-18). Birkhäuser. |
Abstract: | In this note we present a review, some considerations and new results about maps with values in a distribution space and domain in a σ-finite measure space X. Namely, this is a survey about Bessel maps, frames and bases (in particular Riesz and Gel’fand bases) in a distribution space. In this setting, the Riesz-Fischer maps and semi-frames are defined and new results about them are obtained. Some examples in tempered distributions space are examined. |
Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
Appare nelle tipologie: | 2.01 Capitolo o Saggio |
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