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Summability of Fourier Orthogonal Series for Jacobi Weight on a Ball in Rd

Yuan Xu
Transactions of the American Mathematical Society
Vol. 351, No. 6 (Jun., 1999), pp. 2439-2458
Stable URL: http://www.jstor.org/stable/117878
Page Count: 20
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Summability of Fourier Orthogonal Series for Jacobi Weight on a Ball in Rd
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Abstract

Fourier orthogonal series with respect to the weight function (1-|x|2)μ -1/2 on the unit ball in Rd are studied. Compact formulae for the sum of the product of orthonormal polynomials in several variables and for the reproducing kernel are derived and used to study the summability of the Fourier orthogonal series. The main result states that the expansion of a continuous function in the Fourier orthogonal series with respect to (1-|x|2)μ -1/2 is uniformly (C,δ) summable on the ball if and only if $\delta >mh+(d-1)/2$.

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