02-242 Osamu Ogurisu

Supersymmetric analysis of the spectral theory on infinite graphs (35K, LaTeX2e) May 27, 02

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Abstract. We present a new approach to the spectral theory on infinite graphs. We first show that Laplacians on infinite graphs can be treated in a framework of operator theory with supersymmetry. % Using this supersymmetric structure, we rederive in a simple way known results as in Ref.~[T.\ Shirai, Trans.\ Amer.\ Math.\ Soc., \textbf{32} (1999), 115--132] and to obtain new results.

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