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Bounded solutions for the Schr\＂odinger operator on Riemannian manifolds

이용하|김석우
대한수학회 (The Korean Mathematical Society)|2007.08|대한수학회보 (Bulletin of the KMS)|제44권 제3호|pp. 507-516

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Abstract

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.

참고문헌 (10)

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  2. "On Liouville theorems for harmonic functions with nite Dirichlet integral", pp.504~ (1987)
  3. "Dimensions of spaces of harmonic functions translation in Math. Notes 48" (1990)
  4. "Liouville property for Schrodinger operators", 312(4), pp.659~716 (1998)
  5. "Generalized Liouville property for Schrodinger operator onRiemannian manifolds", 238(2), pp.355~387 (2001)
  6. "Rough isometry and energy nite solutions for the Schrodinger operator onRiemannian manifolds", A133(4), pp.855~873 (2003)
  7. "Positive harmonic functions on complete manifolds with nonnega-tive curvature outside a compact set Ann. of Math.", pp.207~ (1987)
  8. "Harmonic functions and the structure of complete manifolds", pp.383~ (1992)
  9. "Spaces of harmonic functions", (2)61(3), pp.789~806 (2000)
  10. "Harmonic functions on complete Riemannian manifolds", pp.28 228~ (1975)

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