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Orthogonal Polynomials on Bubble-Diamond Fractals by Axinn, Elena; Osborne, Calvin; Okoudjou, Kasso A.; Rigatti, Olivia; Shi, Helen is a scholarly article available to read on EtoBox.

What is Orthogonal Polynomials on Bubble-Diamond Fractals about?

We develop a theory of polynomials and, in particular, an analog of the theory of Legendre orthogonal polynomials on the bubble-diamond fractals, a class of fractal sets that can be viewed as the completion of a limit of a sequence of finite graph approximations. In this setting, a polynomial of degree $j$ can be viewed as a multiharmonic function, a solution of the equation $\Delta^{j+1}u=0$. We prove that the sequence of orthogonal polynomials we construct obey a three-term recursion formula. Finally, we present some numerical results about the asymptotics of the coefficients appearing in this three-term recursion formula.

Author

Axinn, Elena; Osborne, Calvin; Okoudjou, Kasso A.; Rigatti, Olivia; Shi, Helen

Published

2024

Language

EN