Translation generated oblique dual frames on locally compact groups
type: Item
instance of: scholarly article
title: Translation generated oblique dual frames on locally compact groups
zbMATH Open document ID: 1547.43002
DOI: 10.1080/03081087.2023.2173718
author: Sudipta Sarkar
author: Niraj K. Shukla
published in: Linear and Multilinear Algebra
publication date: 2024-05-29T00:00:00Z
review text: This paper provides an illuminating unification of a variety of results concerning dual frames in the context of a second countable locally compact group \(\mathcal{G}\) with a distinguished closed abelian subgroup \(\Gamma\). This is done by studying the following general situation: Let \(\mathcal{H}\) be a separable Hilbert space and \((X,\mu_X)\) a \(\sigma\)-finite measure space such that \(L^2(X)\) is separable. The focus is on subsets and subspaces of \(L^2(X,\mathcal{H})\) and relating these to the pointwise almost everywhere corresponding subsets and subspaces of \(\mathcal{H}\). The results obtained in this general situation are then applied back in the group setting.
reviewed by: Keith F. Taylor
Mathematics Subject Classification ID: 43A32
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 46C05
zbMATH DE Number: 7855977
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7855977