On spectral synthesis for contractive \(p\)-norms and Besov spaces
type: Item
instance of: scholarly article
title: On spectral synthesis for contractive \(p\)-norms and Besov spaces
zbMATH Open document ID: 1045.31003
DOI: 10.1023/A:1026365221549
author: Masatoshi Fukushima
author: Toshihiro Uemura
published in: Potential Analysis
publication date: 2004-03-15T00:00:00Z
review text: Let \(F_p\) be a general function space with a contractive \(L_p\)-norm, i.e. we are dealing with norms of the type \[ \int_{(X\times X)\setminus\text{diag}}| u(x)- u(y)|^p\,\nu(dx,dy)+ \int_X| u(x)|^p m(dy). \] For such spaces the following spectral synthesis result is proved: Every quasi-continuous functions in \(F_p\) vanishing quasi-everywhere outside an open set \(G\) can be approximated in this norm by continuous functions in \(F_p\) with compact support in \(G\). This result is applied to contractive Besov spaces of \(d\)-sets in \(\mathbb{R}^N\) and censored stable processes over \(N\)-sets.
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 60J75
zbMATH DE Number: 2057482
zbMATH Keywords: spectral synthesis
zbMATH Keywords: contractive \(L_p\)-norms
zbMATH Keywords: Besov spaces
zbMATH Keywords: censored stable processes
reviewed by: Niels Jacob
MaRDI profile type: Publication
full work available at URL: a:1026365221549
OpenAlex ID: W203421740
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description: scientific article; zbMATH DE number 2057482