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On Approximation By Reproducing Kernel Spaces in Weighted L p Spaces

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Abstract

In this paper, we investigate the order of approximation by reproducing kernel spaces on (−1,1) in weighted L p spaces. We first restate the translation network from the view of reproducing kernel spaces and then construct a sequence of approximating operators with the help of Jacobi orthogonal polynomials, with which we establish a kind of Jackson inequality to describe the error estimate. Finally, The results are used to discuss an approximation problem arising from learning theory.

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Authors and Affiliations

  1. Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, 312000, China

    Baohuai Sheng

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  1. Baohuai Sheng
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Correspondence to Baohuai Sheng.

Additional information

The research is supported by the National Natural Science Foundation under Grant No. 10471130 and the Zhejiang Province Science Foundation under Grant No. Y604003.

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Sheng, B. On Approximation By Reproducing Kernel Spaces in Weighted L p Spaces. Jrl Syst Sci & Complex 20, 623–638 (2007). https://doi.org/10.1007/s11424-007-9061-y

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  • DOI: https://doi.org/10.1007/s11424-007-9061-y

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