Abstract
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 L2, 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. Show more
Publication status
publishedExternal links
Journal / series
Journal of Fourier Analysis and ApplicationsVolume
Pages / Article No.
Publisher
SpringerSubject
Orthogonal polynomials; Sierpinski Gasket; Sobolev orthogonal polynomialsMore
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