Mean convergence of orthogonal Fourier series and interpolating polynomials

Details Mean convergence of orthogonal Fourier series and interpolating polynomials Mean convergence of orthogonal Fourier series and interpolating polynomials

2004-01-29

arxiv.org/abs/math/0401415v1

Mathematics

Numerical Analysis

22 pages

Scientific paper

For a family of weight functions that include the general Jacobi weight functions as special cases, exact condition for the convergence of the Fourier orthogonal series in the weighted $L^p$ space is given. The result is then used to establish a Marcinkiewicz-Zygmund type inequality and to study weighted mean convergence of various interpolating polynomials based on the zeros of the corresponding orthogonal polynomials.

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