Surprisingly, Fourier series on certain fractals can have better
convergence properties than classical Fourier series. This is a
result of the existence of gaps in the spectrum of the Laplacian. In
this work we prove a general criterion for the existence of gaps.
Most of the known examples on which the Laplacians admit spectral
decimation satisfy the criterion. Then we analyze the infinite
family of Vicsek sets, finding an explicit formula for the spectral
decimation functions in terms of Chebyshev polynomials. The
Laplacians on this infinite family of fractals are also shown to
satisfy our criterion and thus have gaps in their spectrum.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OWTU.10012/3435 |
| Date | January 2007 |
| Creators | Zhou, Denglin |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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