APPROXIMATION BY INTERPOLATING POLYNOMIALS IN WEIGHTED SYMMETRIC SMIRNOV SPACES

Abstract

APPROXIMATION BY INTERPOLATING POLYNOMIALS IN WEIGHTED SYMMETRIC SMIRNOV SPACES

Abstract

Let Γ ⊂ C be a closed BR curve without cusps. In this work approximation by complex interpolating polynomials in a Weighted Symmetric Smirnov Space is studied. It is proved that the convergence rate of complex interpolating polynomials and the convergence rate of best approximating algebraic polynomials are the same in the norm of Symmetric Smirnov Spaces.

Keywords

• Curve of bounded rotation,Faber polynomials,Interpolating polynomial,Symmetric Smirnov space,Cauchy singular operator

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