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Discrete Schrödinger operators on a graph

Published online by Cambridge University Press:  22 January 2016

Polly Wee Sy  and
Toshikazu Sunada
Polly Wee Sy
Affiliation:
Department of Mathematics University of the Philippines, Diliman, Quezon City, Philippines
Toshikazu Sunada
Affiliation:
Department of Mathematics University of Tokyo, Tokyo 113, Japan
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In this paper, we study some spectral properties of the discrete Schrödinger operator = Δ + q defined on a locally finite connected graph with an automorphism group whose orbit space is a finite graph.

The discrete Laplacian and its generalization have been explored from many different viewpoints (for instance, see [2] [4]). Our paper discusses the discrete analogue of the results on the bottom of the spectrum established by T. Kobayashi, K. Ono and T. Sunada [3] in the Riemannian-manifold-setting.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 125 , March 1992 , pp. 141 - 150
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1992

References

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