Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces

Authors:
Ben-yu Guo;Li-lian Wang
Affiliations:
Department of Mathematics, Division of Computational Science of E-Institute of Shanghai Universities, Shanghai Normal University, Shanghai 200234, China;Department of Mathematics, Division of Computational Science of E-Institute of Shanghai Universities, Shanghai Normal University, Shanghai 200234, China
Venue:
Journal of Approximation Theory
Year:
2004

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Abstract

Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces are investigated. Some results on orthogonal projections and interpolations are established. Explicit expressions describing the dependence of approximation results on the parameters of Jacobi polynomials are given. These results serve as an important tool in the analysis of numerous quadratures and numerical methods for differential and integral equations.