Sobolev Orthogonal Polynomials on the Sierpinski Gasket
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS(2021)
摘要
We develop a theory of Sobolev orthogonal polynomials on the Sierpiński gasket ( SG ), which is a fractal set that can be viewed as a limit of a sequence of finite graphs. These orthogonal polynomials arise through the Gram–Schmidt orthogonalisation process applied on the set of monomials on SG using several notions of a Sobolev inner products. After establishing some recurrence relations for these orthogonal polynomials, we give estimates for their L^2 , L^∞ , and Sobolev norms, and study their asymptotic behavior. Finally, we study the properties of zero sets of polynomials and develop fast computational tools to explore applications to quadrature and interpolation.
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关键词
Orthogonal polynomials, Sierpinski Gasket, Sobolev orthogonal polynomials
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