SPECTRA OF LAPLACIANS ON FORMS ON AN INFINITE GRAPH

被引：6

作者：

Ayadi, Hela ^{[1
]}

机构：

[1] Univ Nantes, Lab Math Jean Leray, Fac Sci Bizerte, Unite Rech Math & Applicat UR 13ES47, Nantes, France

来源：

OPERATORS AND MATRICES | 2017年 / 11卷 / 02期

关键词：

Infinite weighted graph; discrete Laplacian; Weyl's criterion; spectrum;

D O I：

10.7153/oam-11-37

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the context of infinite weighted graphs, we consider the discrete Laplacians on 0-forms and 1-forms. Using Weyl's criterion, we prove the relation between the nonzero spectrum of Delta(0) and that of Delta(1). Moreover, we give an extension of the work of John Lott to characterize the 0-spectrum of these two Laplacians.

引用

页码：567 / 586

页数：20

共 21 条

[1] The Gauss-Bonnet operator of an infinite graph [J].

Anne, Colette ;

Torki-Hamza, Nabila .

ANALYSIS AND MATHEMATICAL PHYSICS, 2015, 5 (02) :137-159

[2]

AYADI H., 2015, SEMI FREDHO IN PRESS

[3]

Baloudi H., 2015, ARXIV150506109

[4]

DEVERDIERE Y. COLIN, 1998, SPECTRE GRAPHES COUR, V4

[5]

Dodziuk J., 2006, Elliptic operators on infinite graphs. Analysis, P353

[6] Spectral Theory for Discrete Laplacians [J].

Dutkay, Dorin Ervin ;

Jorgensen, Palle E. T. .

COMPLEX ANALYSIS AND OPERATOR THEORY, 2010, 4 (01) :1-38

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

Fujiwara, K .

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

[8] Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds [J].

Grigor'yan, A .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 36 (02) :135-249

[9]

Grigoryan Alexander, 2011, LECT NOTES

[10]

Gromov M., 1993, LONDON MATH SOC LECT, pvii+295

← 1 2 3 →