{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/orthogonal-polynomials-on-bubble-diamond","title":"Orthogonal Polynomials on Bubble-Diamond Fractals","arxiv_id":"2411.16881","date":"2024-11-25","proceeding":null,"authors":["Elena Axinn","Calvin Osborne","Kasso A. Okoudjou","Olivia Rigatti","Helen Shi"],"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 $\\Delta^{j+1}u=0$. We prove that the sequence of orthogonal polynomials we construct obeys a three-term recursion formula.","url_abs":"https://arxiv.org/abs/2411.16881v1","url_pdf":"https://arxiv.org/pdf/2411.16881v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"orthogonal-polynomials-on-bubble-diamond","repo_url":"https://github.com/COsborne25/orthogonal-polynomials-bubble-diamond","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}