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Rough isometry and energy-finite solutions for the Schrödinger operator on Riemannian manifolds

Title
Rough isometry and energy-finite solutions for the Schrödinger operator on Riemannian manifolds
Authors
Kim S.W.Lee Y.H.
Ewha Authors
이용하
SCOPUS Author ID
이용하scopus
Issue Date
2003
Journal Title
Royal Society of Edinburgh - Proceedings A
ISSN
0308-2105JCR Link
Citation
Royal Society of Edinburgh - Proceedings A vol. 133, no. 4, pp. 855 - 873
Indexed
SCI; SCIE; SCOPUS scopus
Document Type
Conference Paper
Abstract
In this paper, we prove that the dimension of the space of bounded energy-finite solutions for the Schrödinger operator is invariant under rough isometries between complete Riemannian manifolds satisfying the local volume condition, the local Poincaré inequality and the local Sobolev inequality. We also prove that the dimension of the space of bounded harmonic functions with finite Dirichlet integral is invariant under rough isometries between complete Riemannian manifolds satisfying the same local conditions. These results generalize those of Kanai, Grigor'yan, the second author, and Li and Tam.
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사범대학 > 수학교육과 > Journal papers
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