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Abstract

The study of self-adjoint operators on fractal spaces has been well developed on specific classes of fractals, such as post-critically finite and finitely ramified. In Part I, we begin by discussing the spectrum of a self-similar Laplacian on a family of post-critically finite fractals, calculating the spectrum for a general member of this family. To complement this we then discuss a source of post-critically finite fractals from self-similar groups that are associated with the Hanoi Towers game and certain modifications of these groups. Part II develops the spectral analysis of a self-adjoint Laplacian on Laakso spaces. The spectrum of this operator is calculated in general with multiplicities and supported by numerical calculations for many specific Laakso spaces.

Details

Title
Diffusions and Laplacians on Laakso, Barlow-Evans, and other fractals
Author
Steinhurst, Benjamin
Year
2010
Publisher
ProQuest Dissertations & Theses
ISBN
978-1-124-04281-7
Source type
Dissertation or Thesis
Language of publication
English
ProQuest document ID
577000075
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.