Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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BOUNDED SOLUTIONS FOR THE $SCHRËDINGER OPERATOR ON RIEMANNIAN MANIFOLDS

  • Kim, Seok-Woo (DEPARTMENT OF MATHEMATICS EDUCATION KONKUK UNIVERSITY) ;
  • Lee, Yong-Hah (DEPARTMENT OF MATHEMATICS EDUCATION EWHA WOMANS UNIVERSITY)
  • Published : 2007.08.31
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Abstract

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

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References

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