Orthogonal Polynomials on Bubble-Diamond Fractals

2024/11/25 by Elena Axinn, Axinn, Elena, Kasso A. Okoudjou +6
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2411.16881

openalex publication_date 2024/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 Δ^j+1u=0. We prove that the sequence of orthogonal polynomials we construct obeys a three-term recursion formula.

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