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 (2021). 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. 625-645). Birkhäuser.
Riesz-Fischer maps, semi-frames and frames in rigged Hilbert spaces
Francesco Tschinke
2021-01-01
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.
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