Papers › Orthogonal Polynomials on Bubble-Diamond Fractals
Orthogonal Polynomials on Bubble-Diamond Fractals
Elena Axinn, Calvin Osborne, Kasso A. Okoudjou, Olivia Rigatti, Helen Shi
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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 Δʲ⁺¹u=0. We prove that the sequence of orthogonal polynomials we construct obeys a three-term recursion formula.
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