Uniqueness of minimal Fourier-type extensions in \(L_1\)-spaces
type: Item
instance of: scholarly article
title: Uniqueness of minimal Fourier-type extensions in \(L_1\)-spaces
zbMATH Open document ID: 1270.41007
author: Grzegorz Lewicki
author: Agnieszka Micek
published in: Monatshefte für Mathematik
publication date: 2013-05-13T00:00:00Z
review text: Let \(Z\) be a so-called \(n\)-circular set in the \(n\)-dimensional complex Euclidean space \(\mathbb{C}^n\) and \(\nu \) be a positive measure on \(Z\). By \(L_1(Z)\), let us denote the space of all \(\nu \)-measurable complex-valued functions on \(Z\) with respect to the usual norm. The problem of a characterization of uniqueness of finite rank Fourier-type minimal extensions in the space \(L_1(Z)\) is considered. This generalizes the main result obtained earlier by the first author.
Mathematics Subject Classification ID: 41A35
Mathematics Subject Classification ID: 41A52
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 6162233
zbMATH Keywords: Fourier projection
zbMATH Keywords: minimal extension
zbMATH Keywords: uniqueness of minimal extensions
reviewed by: D. K. Ugulava
MaRDI profile type: Publication
full work available at URL: s00605-012-0468-8
OpenAlex ID: W1988909316
Wikidata QID: Q59303199
cites work: Norm-one projections onto subspaces of \(\ell _ p\)
cites work: Symmetric spaces with maximal projection constants
cites work: A proof of the Grünbaum conjecture
cites work: Three-dimensional subspace of \(l^{(5)}_\infty\) with maximal projection constant
cites work: The Determination of Minimal Projections and Extensions in L 1
cites work: Q4838510
cites work: On the existence and characterization of minimal projections.
cites work: Approximation theory in tensor product spaces
cites work: Q5620940
cites work: On the Minimal Property of the Fourier Projection
cites work: Q5513421
cites work: Strong uniqueness, Lipschitz continuity, and continuous selections for metric projections in \(L_1\)
cites work: Projections onto hyperplanes in Banach spaces
cites work: Minimal projections in \(\mathcal L_1\)-spaces
cites work: Unique Minimality of Fourier Projections
cites work: Norms of minimal projections
cites work: Q5607459
cites work: Q5607458
cites work: Q4508979
cites work: Fourier-type minimal extensions in real \(L_1\)-space
cites work: Q5443990
cites work: Minimal projections in tensor-product spaces
cites work: Minimal projections in Banach spaces. Problems of existence and uniqueness and their application
cites work: Q3958740
cites work: Q3560388
cites work: Norming points and unique minimality of orthogonal projections
DOI: 10.1007/S00605-012-0468-8
description: scientific article; zbMATH DE number 6162233