Elsevier

Journal of Approximation Theory

Volume 160, Issues 1–2, September–October 2009, Pages 113-134
Journal of Approximation Theory

Characterizations of smoothness of functions in terms of the basis conjugate to Jacobi polynomials

Dedicated to Professor Paul L. Butzer on the occasion of his 80th birthday
https://doi.org/10.1016/j.jat.2008.03.006Get rights and content
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Abstract

By expanding a function fLp((-1,1),(1-s)α(1+s)βds) (1p<) in terms of the basis conjugate to the Jacobi polynomials, the associated generalized translation Tt and the generalized difference T˜t are introduced to define the smoothness of f, respectively, The related Lipschitz classes are characterized by the properties of the Poisson integral near to the boundary.

MSC

42C10
33C45

Keywords

Jacobi expansion
Smoothness
Generalized translation
Generalized difference

Cited by (0)

Supported by the National Natural Science Foundation of China (No. 10571122), the Beijing Natural Science Foundation, the Project of Excellent Young Teachers and the Doctoral Programme Foundation of National Education Ministry of China, and the Project of Beijing Education Committee.