Eigenvalue comparison theorems of the discrete Laplacians for a graph

被引：11

作者：

Urakawa, H ^{[1
]}

机构：

[1] Tohoku Univ, Grad Sch Informat Sci, Math Labs, Sendai, Miyagi 9808577, Japan

来源：

GEOMETRIAE DEDICATA | 1999年 / 74卷 / 01期

关键词：

first eigenvalue; Laplacian; infinite graph; degree;

D O I：

10.1023/A:1005008324245

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a graph theoretic analogue of Cheng's eigenvalue comparison theorems for the Laplacian of complete Riemannian manifolds. As its applications, we determine the infimum of the (essential) spectrum of the discrete Laplacian for infinite graphs.

引用

页码：95 / 112

页数：18

共 17 条

[1] THE SPECTRAL GEOMETRY OF K-REGULAR GRAPHS [J].

BROOKS, R .

JOURNAL D ANALYSE MATHEMATIQUE, 1991, 57 :120-151

[2] EIGENVALUE COMPARISON THEOREMS AND ITS GEOMETRIC APPLICATIONS [J].

CHEN, SY .

MATHEMATISCHE ZEITSCHRIFT, 1975, 143 (03) :289-297

[3]

Cheng SY., 1975, P S PURE MATH, V27.2, P185, DOI DOI 10.1090/PSPUM/027.2/0378003

[4] DIFFERENCE-EQUATIONS, ISOPERIMETRIC INEQUALITY AND TRANSIENCE OF CERTAIN RANDOM-WALKS [J].

DODZIUK, J .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 284 (02) :787-794

[5]

Dodziuk J., 1988, CONT MATH, V73, P25

[6] ON THE ESSENTIAL SPECTRUM OF A COMPLETE RIEMANNIAN MANIFOLD [J].

DONNELLY, H .

TOPOLOGY, 1981, 20 (01) :1-14

[7] PURE POINT SPECTRUM AND NEGATIVE CURVATURE FOR NONCOMPACT MANIFOLDS [J].

DONNELLY, H ;

LI, P .

DUKE MATHEMATICAL JOURNAL, 1979, 46 (03) :497-503

[8] SOME GEOMETRIC ASPECTS OF GRAPHS AND THEIR EIGENFUNCTIONS [J].

FRIEDMAN, J .

DUKE MATHEMATICAL JOURNAL, 1993, 69 (03) :487-525

[9] The Laplacian on rapidly branching trees [J].

Fujiwara, K .

DUKE MATHEMATICAL JOURNAL, 1996, 83 (01) :191-202

[10] Growth and the spectrum of the Laplacian of an infinite graph [J].

Fujiwara, K .

TOHOKU MATHEMATICAL JOURNAL, 1996, 48 (02) :293-302

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