Orthogonal Polynomials on Bubble-Diamond Fractals
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912498697895936 |
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| author | Axinn, Elena Osborne, Calvin Okoudjou, Kasso A. Rigatti, Olivia Shi, Helen |
| author_facet | Axinn, Elena Osborne, Calvin Okoudjou, Kasso A. Rigatti, Olivia Shi, Helen |
| contents | 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 $Δ^{j+1}u=0$. We prove that the sequence of orthogonal polynomials we construct obeys a three-term recursion formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16881 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orthogonal Polynomials on Bubble-Diamond Fractals Axinn, Elena Osborne, Calvin Okoudjou, Kasso A. Rigatti, Olivia Shi, Helen Functional Analysis 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 $Δ^{j+1}u=0$. We prove that the sequence of orthogonal polynomials we construct obeys a three-term recursion formula. |
| title | Orthogonal Polynomials on Bubble-Diamond Fractals |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2411.16881 |