Mean convergence of orthogonal Fourier series and interpolating polynomials. (English) Zbl 1094.42028
For a family of weight functions that include the general Jacobi weight functions as special cases, exact conditions for the convergence of the Fourier orthogonal series in the weighted \(L^{p}\) space are 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.
Reviewer: Wolfram Koepf (Kassel)
MSC:
42C10 | Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) |
33C50 | Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable |