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초록· 키워드
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LetM be a complete Riemannian manifold and L be a Schro-dinger operator on M . We prove that ifM has nitely many L-nonpara-bolic ends, then the space of bounded L-harmonic functions on M hasthe same dimension as the sum of dimensions of the spaces of boundedL-harmonic functions on each L-nonparabolic end, which vanish at theboundary of the end.
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참고문헌 (10)
참고문헌 신청
/ 1975 / Harmonic functions on complete Riemannian manifolds : 28 228 ~
/ 1987 / On Liouville theorems for harmonic functions with nite Dirichlet integral : 504 ~
/ 1987 / On the set of positive solutions of the Laplace-Beltrami equationon Riemannian manifolds of a special form : 60 ~
/ 1987 / Positive harmonic functions on complete manifolds with nonnega-tive curvature outside a compact set Ann. of Math. : 207 ~
/ 1990 / Dimensions of spaces of harmonic functions translation in Math. Notes 48
/ 1987 / On Liouville theorems for harmonic functions with nite Dirichlet integral : 504 ~
/ 1987 / On the set of positive solutions of the Laplace-Beltrami equationon Riemannian manifolds of a special form : 60 ~
/ 1987 / Positive harmonic functions on complete manifolds with nonnega-tive curvature outside a compact set Ann. of Math. : 207 ~
/ 1990 / Dimensions of spaces of harmonic functions translation in Math. Notes 48
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