Spectral synthesis in Sobolev weighted spaces
type: Item
instance of: scholarly article
title: Spectral synthesis in Sobolev weighted spaces
zbMATH Open document ID: 0851.46025
DOI: 10.1007/BF02110746
author: N. O. Belova
published in: Mathematical Notes
publication date: 1996-11-11T00:00:00Z
review text: The author announces the following result: Theorem 1. Let \(f\) belong to the weighted Sobolev space \(W^m_p (\mathbb{R}^N, w)\), where \(1< p< \infty\) and the weight \(w\) belongs to the Muckenhoupt's class \(A_p\). In addition, let \(K\subset \mathbb{R}^N\) be a closed set and \(D^\alpha f|_K=0\) for \(0\leq |\alpha |\leq m-1\). Then for any \(\varepsilon>0\) there exists a function \(\omega\), \(0\leq \omega\leq 1\), such that \(\omega (x)=1\) in a neighborhood of \(K\) and \(|\omega f\mid W_p^m (\mathbb{R}^N, w)|\leq \varepsilon\). As a corollary she gets a uniqueness theorem for the Dirichlet problem of the polyharmonic equation \(\Delta_m n=0\) in weighted Sobolev spaces.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 43A45
zbMATH DE Number: 830714
zbMATH Keywords: weighted Sobolev space
zbMATH Keywords: Muckenhoupt's class
zbMATH Keywords: uniqueness theorem
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: polyharmonic equation
reviewed by: Josef Wloka
MaRDI profile type: Publication
cites work: Approximation in the mean by solutions of elliptic equations
cites work: Two approximation problems in function spaces
cites work: Spectral synthesis in Sobolev spaces and uniqueness of solutions of the Dirichlet problem
cites work: Approximation in L p by Solutions of Elliptic Partial Differential Equations
cites work: Q5802809
cites work: DIRICHLET SPACES
cites work: Quasi topologies and rational approximation
cites work: Q3922920
cites work: Q3353415
full work available at URL: https://doi.org/10.1007/bf02110746
OpenAlex ID: W2089236176
description: scientific article; zbMATH DE number 830714