Mathematics – Numerical Analysis
Scientific paper
2004-01-29
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.
Vertesi P.
Xu Yuan
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