2011/10/07 by Kasso A. Okoudjou, Robert S. Strichartz, Okoudjou, Kasso A. +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #28A80 #33A99 #33F05 #42C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractal and DNA sequence analysis #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #math.CA #msc:28A80 #msc:33A99 #msc:33F05 #msc:42C05
paper · pdf · doi:10.48550/arxiv.1110.1554
29 pages, 10 figures, 2 tables. Include short version of previous section 5 in subsection 4.4; correct typos, reduce the number of figures
openalex publication_date 2011/10/07 · arxiv created 2012/07/09 · arxiv updated 2012/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The construction of a Laplacian on a class of fractals which includes the Sierpinski gasket (\bf SG) has given rise to an intensive research on analysis on fractals. For instance, a complete theory of polynomials and power series on SG has been developed by one of us and his coauthors. We build on this body of work to construct certain analogs of classical orthogonal polynomials (OP) on SG. In particular, we investigate key properties of these OP on SG, including a three-term recursion formula and the asymptotics of the coefficients appearing in this recursion. Moreover, we develop numerical tools that allow us to graph a number of these OP. Finally, we use these numerical tools to investigate the structure of the zero and the nodal sets of these polynomials.