Boundary Area Growth and the Spectrum of Discrete Laplacian
- Cite this article as:
- Higuchi, Y. Annals of Global Analysis and Geometry (2003) 24: 201. doi:10.1023/A:1024733021533
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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.