Beyond frames: semi-frames and reproducing pairs
type: Item
instance of: scholarly article
title: Beyond frames: semi-frames and reproducing pairs
zbMATH Open document ID: 1421.42017
DOI: 10.1007/978-3-319-97175-9_2
publication date: 2019-07-11T00:00:00Z
review text: The authors study semi-frames and reproducing pairs. A variety of results involving reproducing pairs are given with few results involving semi-frames. A result regarding upper semi-frames and lower semi-frames is given. Duality properties of the spaces generated by weakly measurable functions (pre-Hilbert spaces) are discussed and few results regarding reproducing pairs are proved. The existence of a reproducing pair and the non-uniqueness are proved, together with examples in cases of discrete frames and continuous frames. Reproducing pairs and partial inner product spaces (PIP-spaces) are discussed and some results are proved. Some results regarding reproducing pairs in genuine PIP-spaces (with lattices of Banach spaces and Hilbert spaces) are obtained. The cases of a Hilbert scale and of \(L^p\) spaces are considered and discussed through examples. For the entire collection see [Zbl 1411.00032].
reviewed by: Virender
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 7079457
zbMATH Keywords: frames
zbMATH Keywords: upper semi-frames
zbMATH Keywords: lower semi-frames
zbMATH Keywords: reproducing pairs
zbMATH Keywords: partial inner product sapces
author: J. P. Antoine
author: Camillo Trapani
MaRDI profile type: Publication
full work available at URL: 978-3-319-97175-9 2
OpenAlex ID: W2769890263
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description: scientific article; zbMATH DE number 7079457