Mean convergence of hermite interpolation revisited

Vértesi, P.; Xu, Yuan

doi:10.1007/bf01876225

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“…Since then this result has been extended in several directions, to other interpolation processes and to more general weight functions (see, for example, [5,6,10,11,13] and the reference therein). It turned out [13] that one way of proving such results is to use a Marcinkiewicz-Zygmund type inequality.…”

Section: Introductionmentioning

confidence: 99%

Mean convergence of orthogonal Fourier series and interpolating polynomials

2005

Acta Math Hung

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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.

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Section: Introductionmentioning

confidence: 99%

Mean convergence of orthogonal Fourier series and interpolating polynomials

2005

Acta Math Hung

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The Simultaneous Approximation of Quasi-Hermite Interpolation on the Weighted Mean Norm

Ran

Wang

2009

Int. J. Wavelets Multiresolut Inf. Process.

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In commemoration of the 80th birthday anniversary of Professor Yongsheng SunWe research the simultaneous approximation problem of the quasi-Hermite interpolation that based on the zeros of Chebyshev polynomials under weighted Lp-norm where our estimation is sharp.Are the conditions in Theorem A necessary? It is so in some cases. For example, if w(x) = 1 √ 1−x 2 , m = 2, r = s = 0, then it is easy to verify that for Int. J. Wavelets Multiresolut Inf. Process. 2009.07:825-837. Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/21/15. For personal use only.

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