Premium
Limiting absorption principle on manifolds having ends with various measure growth rate limits
Author(s) -
Kumura Hironori
Publication year - 2013
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pds057
Subject(s) - mathematics , limiting , mathematical analysis , limit (mathematics) , riemannian manifold , laplace–beltrami operator , measure (data warehouse) , resolvent , infinity , operator (biology) , laplace operator , manifold (fluid mechanics) , pure mathematics , p laplacian , mechanical engineering , biochemistry , chemistry , repressor , database , computer science , transcription factor , engineering , gene , boundary value problem
The purpose of this paper is to discuss the properties of the resolvent of the Laplace–Beltrami operator on a noncompact complete Riemannian manifold with various ends each of which has a different limit of the growth rate of the Riemannian measure at infinity, in particular, focusing on the limiting absorption principle. As a result, we will obtain the absolute continuity of the Laplace–Beltrami operator.