Annals of Global Analysis and Geometry

, Volume 24, Issue 3, pp 201–230

Boundary Area Growth and the Spectrum of Discrete Laplacian

  • Yusuke Higuchi

DOI: 10.1023/A:1024733021533

Cite this article as:
Higuchi, Y. Annals of Global Analysis and Geometry (2003) 24: 201. doi:10.1023/A:1024733021533


We introduce the boundary area growth as a new quantity for an infinite graph. Using this, we give some upper bounds for the bottom of the spectrum of the discrete Laplacian which relates closely to the transition operator. We also give some applications and examples.

discrete spectral geometry discrete Laplacian growth function 

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Yusuke Higuchi
    • 1
  1. 1.Mathematics Laboratories, College of Arts and SciencesShowa UniversityFujiyoshida, YamanashiJapan

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