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Boundary Area Growth and the Spectrum of Discrete Laplacian

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Abstract

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.

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Authors and Affiliations

  1. Mathematics Laboratories, College of Arts and Sciences, Showa University, 4562 Kamiyoshida, Fujiyoshida, Yamanashi, 403-0005, Japan

    Yusuke Higuchi

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  1. Yusuke Higuchi
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Higuchi, Y. Boundary Area Growth and the Spectrum of Discrete Laplacian. Annals of Global Analysis and Geometry 24, 201–230 (2003). https://doi.org/10.1023/A:1024733021533

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