Diffusions and Laplacians on Laakso, Barlow-Evans, and other fractals | Posted on:2011-06-25 | Degree:Ph.D | Type:Dissertation | University:University of Connecticut | Candidate:Steinhurst, Benjamin | Full Text:PDF | GTID:1440390002464822 | Subject:Mathematics | Abstract/Summary: | | 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. | Keywords/Search Tags: | Laakso, Fractals, Spaces | | Related items |
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