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Limiting Absorption Principle for Singularly Perturbed Operators
Author(s) -
Renger Walter
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200108)228:1<163::aid-mana163>3.0.co;2-v
Subject(s) - limiting , mathematics , eigenvalues and eigenvectors , operator (biology) , domain (mathematical analysis) , mathematical analysis , absorption (acoustics) , limit (mathematics) , pure mathematics , quantum mechanics , physics , chemistry , mechanical engineering , biochemistry , repressor , transcription factor , acoustics , engineering , gene
Abstract Given an operator H 1 for which a limiting absorption principle holds, we study operators H 2 which are produced by perturbing H 1 in the sense that the difference between some powers of the resolvents is compact.We show that (except for possibly a discrete set of eigenvalues) a limiting absorption principle holds for H 2 . We apply this theory to study potential and domain perturbations of Feller operators. While our theory mostly reproduces known results in the case of potential perturbations, for domain perturbations we get results which appear to be new.