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Orthogonal Polynomials on the Sierpinski Gasket

A complete theory of polynomials and power series has been developed on the Sierpinski Gasket (SG). We build on this work by constructing certain analogs of orthogonal polynomials (OP) on SG. In particular we construct a three-term recurrence formula for the OP, and investigate the asymptotics of the coefficients in this recurrence relation. We also study the zero sets of the OP, as well as the dynamics of the values of the OP at fixed points in SG.

This website displays the results, as well as provides the programs used to create these polynomials.

This research was a collaborative effort between Kasso Okoudjou, Robert Strichartz, and Elizabeth Tuley; in part at the Cornell REU in Summer 2009.