Eigenvalue distribution of semi-elliptic operators in anisotropic Sobolev spaces
type: Item
instance of: scholarly article
title: Eigenvalue distribution of semi-elliptic operators in anisotropic Sobolev spaces
zbMATH Open document ID: 1175.47018
DOI: 10.4171/ZAA/1383
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2009-05-05T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: This paper begins by introducing some basic notation and concepts used in the study of anisotropic spaces. It then proceeds to formulate some definitions, after which it lists some important properties of anisotropic function spaces of Besov and Sobolev type. The paper then deals with the concepts of anisotropic \(d\)-sets, and the approximation numbers of related embeddings and trace operators. The paper concludes by giving two-sided estimates for the asymptotic behaviour of the eigenvalues for a semi-elliptic differential operator, and of a special trace operator on an anisotropic \(d\)-set.
reviewed by: Alan Jeffrey
Mathematics Subject Classification ID: 47B06
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 5550897
zbMATH Keywords: anisotropic function spaces
zbMATH Keywords: approximation numbers
zbMATH Keywords: semi-elliptic operators
zbMATH Keywords: traces
author: Erika Tamăsi
MaRDI profile type: Publication
cites work: Q4875881
cites work: Spectral theory for isotropic fractal drums
cites work: Q3764747
cites work: The Distribution of Eigenfrequencies of Anisotropic Fractal Drums
cites work: The behaviour of the eigenvalues for a class of operators related to some self-affine fractals in \(\mathbb{R}^2\).
cites work: Eigenvalue distribution of some fractal semi-elliptic differential operators
cites work: Q3797996
cites work: Weyl's problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals
cites work: Q4273496
cites work: Boundedness of anisotropic pseudo-differential operators in function spaces of Besov-Hardy-Sobolev type
cites work: Q4318932
cites work: The eigenvalue behaviour for the boundary value problems related to self- similar measures on \(\mathbb{R}^ d\)
cites work: Q3810338
cites work: Spectral Properties of Some Semi - Elliptic Operators in Lp
cites work: On a Spectral Problem Related to Self-Similar Measures
cites work: Problems in harmonic analysis related to curvature
cites work: Decomposition Methods for Function Spaces ofBp,qs Type andFp,qs Type
cites work: Anisotropic Besov spaces and approximation numbers of traces on related fractal sets
cites work: Q4114272
cites work: Q3341265
cites work: Q3336200
cites work: Q3997830
cites work: Approximation numbers in function spaces and the distribution of eigenvalues of some fractal elliptic operators
cites work: Q5481429
cites work: Q3748827
description: scientific article; zbMATH DE number 5550897