Spectral analysis on Barlow and Evans' projective limit fractals
type: Item
instance of: scholarly article
title: Spectral analysis on Barlow and Evans' projective limit fractals
zbMATH Open document ID: 1469.81023
DOI: 10.4171/JST/337
author: Alexander Teplyaev
author: Benjamin A. Steinhurst
published in: Journal of Spectral Theory
publication date: 2021-08-03T00:00:00Z
review text: Summary: We review the projective limit construction of a state space for a Markov process use by Barlow and Evans. On this state space we construct a projective limit Dirichlet form in a process analogous to Barlow and Evan's construction of a Markov process. Then we study the spectral properties of the corresponding Laplacian using the projective limit construction. For some examples, such as the Laakso spaces and a Sierpiński pâte à choux, one can develop a complete spectral theory, including the eigenfunction expansions that are analogous to Fourier series. In addition, we construct connected fractal spaces isospectral to the fractal strings of Lapidus and van Frankenhuijsen. Our work is motivated by recent progress in mathematical physics on fractals.
Mathematics Subject Classification ID: 81Q35
Mathematics Subject Classification ID: 81S25
Mathematics Subject Classification ID: 81P16
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 46M40
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 81Q12
zbMATH DE Number: 7377512
zbMATH Keywords: spectral theory on fractals
zbMATH Keywords: Dirichlet forms
zbMATH Keywords: Laplacians
zbMATH Keywords: inverse or projective limits
MaRDI profile type: Publication
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Spectral analysis on Barlow and Evans' projective limit fractals (full work available at URL)
full work available at URL: https://doi.org/10.4171/jst/337

Spectral analysis on Barlow and Evans' projective limit fractals (OpenAlex ID)
OpenAlex ID: W3132921328