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ROUGH ISOMETRY AND THE SPACE OF BOUNDED ENERGY FINITE SOLUTIONS OF THE SCHR¨ODINGER OPERATOR ON GRAPHS

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대한수학회 (The Korean Mathematical Society)|2010.10|대한수학회논문집 (Communications of the KMS)|제25권 제4호|pp. 609-614

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참고문헌

키워드

infinite graphSchr¨odinger operatorbounded energy finite solutionrough isometry
주제분류수학

초록

We prove that if graphs of bounded degree are roughly isometric to each other, then the spaces of bounded energy finite solutions of the Schr¨odinger operator on the graphs are isomorphic to each other. This is a direct generalization of the results of Soardi [5] and of Lee [3].

Abstract

We prove that if graphs of bounded degree are roughly isometric to each other, then the spaces of bounded energy finite solutions of the Schr¨odinger operator on the graphs are isomorphic to each other. This is a direct generalization of the results of Soardi [5] and of Lee [3].

참고문헌 (6)

  1. M. Kanai, "Rough isometries, and combinatorial approximations of geometries of noncompact Riemannian manifolds", J. Math. Soc., 37(3), pp.391~413 (1985)
  2. T. Kayano, "Boundary limit of discrete Dirichlet potentials", Hiroshima Math. J., 14(2), pp.401~406 (1984)
  3. Y. H. Lee, "Rough isometry and energy finite solutions of the Schrodinger operator on graphs", Discrete Math., 263(1), pp.167~177 (2003)
  4. H. L. Royden, "Harmonic functions on open Riemann surfaces", Trans. Amer. Math. Soc., 73, pp.40~94 (1952)
  5. P. M. Soardi, "Rough isometries and Dirichlet finite harmonic functions on graphs", Proc. Amer. Math. Soc., 119(4), pp.1239~1248 (1993)
  6. M. Yamasaki, "Ideal boundary limit of discrete Dirichlet functions", Hiroshima Math. J., 16(2), pp.353~360 (1986)

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