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초록· 키워드
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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].
목차
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참고문헌 (6)
참고문헌 신청
H. L. Royden / 1952 / Harmonic functions on open Riemann surfaces / Trans. Amer. Math. Soc. 73 : 40 ~ 94
M. Kanai / 1985 / Rough isometries, and combinatorial approximations of geometries of noncompact Riemannian manifolds / J. Math. Soc. 37 (3) : 391 ~ 413
M. Yamasaki / 1986 / Ideal boundary limit of discrete Dirichlet functions / Hiroshima Math. J. 16 (2) : 353 ~ 360
P. M. Soardi / 1993 / Rough isometries and Dirichlet finite harmonic functions on graphs / Proc. Amer. Math. Soc. 119 (4) : 1239 ~ 1248
T. Kayano / 1984 / Boundary limit of discrete Dirichlet potentials / Hiroshima Math. J. 14 (2) : 401 ~ 406
M. Kanai / 1985 / Rough isometries, and combinatorial approximations of geometries of noncompact Riemannian manifolds / J. Math. Soc. 37 (3) : 391 ~ 413
M. Yamasaki / 1986 / Ideal boundary limit of discrete Dirichlet functions / Hiroshima Math. J. 16 (2) : 353 ~ 360
P. M. Soardi / 1993 / Rough isometries and Dirichlet finite harmonic functions on graphs / Proc. Amer. Math. Soc. 119 (4) : 1239 ~ 1248
T. Kayano / 1984 / Boundary limit of discrete Dirichlet potentials / Hiroshima Math. J. 14 (2) : 401 ~ 406
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