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BOUNDED SOLUTIONS FOR THE \$SCHRËDINGER OPERATOR ON RIEMANNIAN MANIFOLDS

Title & Authors
BOUNDED SOLUTIONS FOR THE \$SCHRËDINGER OPERATOR ON RIEMANNIAN MANIFOLDS
Kim, Seok-Woo; Lee, Yong-Hah;

Abstract
Let M be a complete Riemannian manifold and L be a $\small{Schr\"{o}dinger}$ operator on M. We prove that if M has finitely many L-nonparabolic ends, then the space of bounded L-harmonic functions on M has the same dimension as the sum of dimensions of the spaces of bounded L-harmonic functions on the L-nonparabolic end, which vanish at the boundary of the end.
Keywords
$\small{Schr\"{o}dinger}$ operator;L-harmonic function;L-massive set;end;
Language
English
Cited by
References
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