Isaac Scientific Publishing

Journal of Advances in Applied Mathematics

Lp-Convergence of Orthogonal Polynomial Expansions for Exponential Weights

Download PDF (397.5 KB) PP. 91 - 103 Pub. Date: July 1, 2020

DOI: 10.22606/jaam.2020.53001

Author(s)

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

Abstract

Let R = (−∞,∞), and let Q ∈ C1(R) : R → [0,∞) be an even function which is an exponent. We consider the weight w(x) = e −Q(x), x ∈ R. Let us denote the partial sum of Fourier series for a function f by sn(f; x) := sn(f;w2; x), and the de la Vall´ee Poussin mean of f by vn(f) := vn(f;w2). Then we investigate the convergences of sn(f) and vn(f) with w(x).

Keywords

orthogonal polynomial expansions

References

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[9] R. Sakai and N. Suzuki, Mollification of exponential weights and its application to the Markov-Bernstein inequality, Pioneer J. of Math., Vol.7, no.1 (2013) 83-101.