The existence of a point spectral radius for pseudodifferential operators
type: Item
instance of: scholarly article
title: The existence of a point spectral radius for pseudodifferential operators
zbMATH Open document ID: 0897.35081
author: Ha Huy Bang
published in: Doklady Mathematics
publication date: 1998-10-19T00:00:00Z
review text: Let \(M_{K \varphi}\) denote the Orlicz space defined by a Young function \(\Phi\), whose elements \(f\) have the property that \(\text{supp} \widehat f\subset K\), \(K\) a compact set in \(\mathbb{R}^n\). The author introduces an algebra of \(\psi DO\) such that for any element \(A(D)\) of this algebra there always exists the limit \(\lim_{m\to \infty} \| A^m(D)f \|^{1/m}\) for any \(f\in M_{K \varphi}\), where \(\| \cdot \|\) denotes the norm in \(M_{K \varphi}\). The spectral radius of the \(\psi DO\) of the introduced algebra is evaluated and, as applications, some convex and non-convex versions of the Paley-Wiener theorem are obtained.
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 1122789
zbMATH Keywords: Orlicz space
zbMATH Keywords: Young function
zbMATH Keywords: algebra
zbMATH Keywords: spectral radius
zbMATH Keywords: Paley-Wiener theorem
reviewed by: Viorel Iftimie
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1122789