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Representation of Reproducing Kernels and the Lebesgue Constants on the Ball

✍ Scribed by Yuan Xu

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 149 KB
Volume: 112
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.2001.3597

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✦ Synopsis

For the weight function (1 -||x|| 2 ) m -1/2 on the unit ball, a closed formula of the reproducing kernel is modified to include the case -1/2 < m < 0. The new formula is used to study the orthogonal projection of the weighted L 2 space onto the space of polynomials of degree at most n, and it is proved that the uniform norm of the projection operator has the growth rate of n (d -1)/2 for m < 0, which is the smallest possible growth rate among all projections, while the rate for m \ 0 is n m+(d -1)/2 .

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