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Generalized Liouville property for Schr\＂odinger operator on graphs

Generalized Liouville property for Schr\"odinger operator on graphs

Seok Woo Kim|Yong Hah Lee
대한수학회 (The Korean Mathematical Society)|2005.07|대한수학회논문집 (Communications of the KMS)|제20권 제3호|pp. 521-529

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Abstract

We prove that the dimension of the space of posi-tive (bounded, respectively) solutions for the SchrÄodinger operator whose potential q is nonnegative on a graph with q-regular ends is equal to the number of ends (q- nonparabolic ends, respectively).

참고문헌 (7)

  1. "A strong Liouville theorem forp-harmonic func-tions on graphs", 22, pp.205~226 (1997)
  2. "Rough isometries and the parabolicity of riemannian manifolds", 38, pp.227~238 (1986)
  3. "Generalized Liouville property for Schrodinger operatoron Riemannian manifolds", 238, pp.355~387 (2001)
  4. "Rough isometry and Dirichlet nite harmonic functions Riemannianmanifolds", 99, pp.311~328 (1999)
  5. "Rough isometry and energy nite solutions of the Schrodinger operatoron graphs", 263, pp.167~177 (2003)
  6. "Rough isometries and energy nite harmonic functions on graphs", 119, pp.1239~1248 (1993)
  7. "Rough isometries and energy nite harmonic functions on graphs", 119, pp.1239~1248 (1993)

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