Isaac Scientific Publishing

Journal of Advances in Applied Mathematics

A Study of Weighted Polynomial Approximations for Orthogonal Polynomial Expansion

Download PDF (642.7 KB) PP. 173 - 195 Pub. Date: July 31, 2017

DOI: 10.22606/jaam.2017.23007

Author(s)

  • Ryozi Sakai*
    Department of Mathematics, Meijo University, Tenpaku-ku, Nagoya 468-8502, Japan

Abstract

We investigate weighted polynomial approximations. Especially, we will study some facts related to the Fourier-type orthogonal expansion and the de la Vall´ee Poussin means. Then the estimate of the modulus of smoothness is important. To complete the theorems we need the Nikolskii-type inequality, higher order derivatives of approximation polynomials, the function with bounded variation, and others.

Keywords

Fourier-type orthogonal expansions, De la Vall´ee Poussin means, Modulus of smoothness.

References

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[9] K. Itoh, R. Sakai and N. Suzuki, The de la Vall′ee Poussin Mean and Polynomial Appoximation for Exponential Weight, International Journal of Analysis, 2015, Article ID 706930, 8 pages, (2015).

[10] K. Itoh, R. Sakai and N. Suzuki, An estimate for derivative of the de la Vall′ee Poussin mean, Math. J. Ibaraki Univ. 47 (2015), 1-18.

[11] K. Itoh, R. Sakai and N. Suzuki, Uniform convergence of orthogonal polynomial expansions for exponential weights, preprint.

[12] K. Itoh, R. Sakai and N. Suzuki, Polynomial approximation for absolutely continuous functions, accepted by Tohoku Math. Journal.