BOUNDED SOLUTIONS FOR THE $SCHRËDINGER OPERATOR ON RIEMANNIAN MANIFOLDS

Seok-Woo Kim, Yong-Hah Lee

Type: Article

Publication Date: 2007-08-31

Citations: 0

DOI: https://doi.org/10.4134/bkms.2007.44.3.507

Abstract

Let M be a complete Riemannian manifold and L be a <TEX>$Schr\"{o}dinger$</TEX> 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.

Locations

Bulletin of the Korean Mathematical Society - View - PDF

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Works Cited by This (5)

Action	Title	Year	Authors
+	Harmonic functions on complete riemannian manifolds	1975	Shing‐Tung Yau
+	Positive Harmonic Functions on Complete Manifolds with Non-Negative Curvature Outside a Compact Set	1987	Peter Li Luen-Fai Tam
+	A Liouville property for Schrödinger operators	1998	Alexander Grigor’yan Wolfhard Hansen
+	Generalized Liouville property for Schrödinger operator on Riemannian manifolds	2001	Seok Woo Kim Yong Hah Lee
+	Spaces of Harmonic Functions	2000	Chiung-Jue Anna Sung Luen-Fai Tam Jiaping Wang