On the spectral synthesis property and its application to partial differential equations
type: Item
instance of: scholarly article
title: On the spectral synthesis property and its application to partial differential equations
zbMATH Open document ID: 0767.47037
DOI: 10.1007/BF02384864
author: Kanghui Guo
published in: Arkiv för Matematik
publication date: 1993-01-16T00:00:00Z
review text: For a closed subset \(M\subset\mathbb{R}^ n\) denote \[ \begin{aligned} I(M) &= \{f|\;\widehat{f}\in L^ 1(\mathbb{R}^ n),\;f\mid M=0\},\\ J^ k(M) &= \{f|\;f\in C_ 0^ k(\mathbb{R}^ n),\;f\mid M=0\}.\end{aligned} \] The main result of the paper is Theorem. Let \(k\geq n+2\). If \(M\) is a compact \(C^ k\)-hypersurface in \(\mathbb{R}^ n\) with non-vanishing Gaussian curvature, then \(\overline {J^ k(M)} =I(M)\) where the closure is taken in the Fourier transformed \(L^ 1\)-norm. As an application, a uniqueness property for partial differential equations with constant coefficients is proved.
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 43A45
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 91593
zbMATH Keywords: spectral synthesis
zbMATH Keywords: PDE with constant coefficients
zbMATH Keywords: \(C^ k\)-hypersurface
zbMATH Keywords: non-vanishing Gaussian curvature
zbMATH Keywords: partial differential equations with constant coefficients
reviewed by: Christian Bär
MaRDI profile type: Publication
cites work: Q5582639
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description: scientific article; zbMATH DE number 91593