Spectral analysis on infinite Sierpiński gaskets
type: Item
instance of: scholarly article
title: Spectral analysis on infinite Sierpiński gaskets
zbMATH Open document ID: 0924.58104
author: Alexander Teplyaev
published in: Journal of Functional Analysis
publication date: 1999-11-08T00:00:00Z
review text: The paper is devoted to the spectral properties of the Laplacian on infinite Sierpiński gaskets. It is proved that the Laplacian with the Neumann boundary condition has pure point spectrum. Moreover, the set of eigenfunctions with compact support is complete. The same is true if the infinite Sierpiński gasket has no boundary, but is false for the Laplacian with the Dirichlet boundary condition. The spectra are found explicitly. The results are based on new formulas for eigenprojectors of the discrete Laplacians on finite Sierpiński pre-gaskets.
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 35S99
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 60J35
zbMATH DE Number: 1268055
zbMATH Keywords: fractal
zbMATH Keywords: fractal graph
zbMATH Keywords: Laplacian
zbMATH Keywords: Sierpiński gasket
zbMATH Keywords: pre-gasket
reviewed by: Anatoly N. Kochubei
MaRDI profile type: Publication
full work available at URL: jfan.1998.3297
OpenAlex ID: W2127863462
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DOI: 10.1006/JFAN.1998.3297
description: scientific article; zbMATH DE number 1268055