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arXiv · 1110.1554

Orthogonal Polynomials on the Sierpinski Gasket

Kasso A. Okoudjou·Robert S. Strichartz·Elizabeth K. Tuley
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Abstract

The construction of a Laplacian on a class of fractals which includes the Sierpinski gasket ({\bf $SG$}) has given rise to an intensive research on analysis on fractals. For instance, a complete theory of polynomials and power series on $SG$ has been developed by one of us and his coauthors. We build on this body of work to construct certain analogs of classical orthogonal polynomials (OP) on $SG$. In particular, we investigate key properties of these OP on $SG$, including a three-term recursion formula and the asymptotics of the coefficients appearing in this recursion. Moreover, we develop numerical tools that allow us to graph a number of these OP. Finally, we use these numerical tools to investigate the structure of the zero and the nodal sets of these polynomials.

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BibTeXRIS

Kasso A. Okoudjou, Robert S. Strichartz, Elizabeth K. Tuley. 2012-07-09. Orthogonal Polynomials on the Sierpinski Gasket. https://arxiv.org/abs/1110.1554

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