Compactness for the -Neumann problem: a functional analysis approach

We characterize compactness of the -Neumann operator for a smoothly bounded pseudoconvex domain and in the setting of weighted L 2 -spaces on . For this purpose we use a description of relatively compact subsets of L 2 -spaces. We also point out how to use this method to show that property (P) impli...

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Bibliographic Details
Published in:Collectanea mathematica (Barcelona) Vol. 62; no. 2; pp. 121 - 129
Main Author: Haslinger, Friedrich
Format: Journal Article
Language:English
Published: Milan Springer Milan 01.05.2011
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
35J10
Primary 32W05
Neumann problem
Secondary 32A36
Sobolev spaces
Compactness
ISSN:0010-0757, 2038-4815
Online Access:Get full text
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Summary:We characterize compactness of the -Neumann operator for a smoothly bounded pseudoconvex domain and in the setting of weighted L 2 -spaces on . For this purpose we use a description of relatively compact subsets of L 2 -spaces. We also point out how to use this method to show that property (P) implies compactness for the -Neumann operator on a smoothly bounded pseudoconvex domain.
ISSN:0010-0757
2038-4815
DOI:10.1007/s13348-010-0013-9