Asymptotic Formulae for Linear Combinations of Generalized Sampling Operators

被引：33

作者：

Bardaro, Carlo ^{[1
]}

Mantellini, Ilaria ^{[1
]}

机构：

[1] Univ Perugia, Dept Math & Informat, I-06123 Perugia, Italy

来源：

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 2013年 / 32卷 / 03期

关键词：

Voronovskaja-type formula; moments; generalized sampling operators; K-functional; APPROXIMATION; THEOREMS;

D O I：

10.4171/ZAA/1485

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give some Voronovskaja formula for linear combinations of generalized sampling operators and we furnish also a quantitative version in terms of the classical Peetre K-functional. This provides a better order of approximation in the asymptotic formula. We apply the general theory to various kernels: Bochner-Riesz kernel, translates of B-splines and Jackson type kernel.

引用

页码：279 / 298

页数：20

共 30 条

[1]

Altomare F., 2010, SURVEYS APPROXIMATIO, V6, P92

[2]

Anastassiou G.A., 2000, Approximation Theory

[3] Uniform convergence with rates for smooth Poisson-Cauchy-type singular integral operators [J].

Anastassiou, George A. ;

Mezei, Razvan A. .

MATHEMATICAL AND COMPUTER MODELLING, 2009, 50 (11-12) :1553-1570

[4]

Bardaro C., 2007, Sampling Theory in Signal and Image Processing, V6, P29

[5]

Bardaro C., 2011, East J. Approx., V17, P181

[6] On the Iterates of Mellin-Fejer Convolution Operators [J].

Bardaro, Carlo ;

Mantellini, Ilaria .

ACTA APPLICANDAE MATHEMATICAE, 2012, 121 (01) :213-229

[7] On Voronovskaja formula for linear combinations of Mellin-Gauss-Weierstrass operators [J].

Bardaro, Carlo ;

Mantellini, Ilaria .

APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (20) :10171-10179

[8] ON CONVERGENCE PROPERTIES FOR A CLASS OF KANTOROVICH DISCRETE OPERATORS [J].

Bardaro, Carlo ;

Mantellini, Ilaria .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2012, 33 (04) :374-396

[9] Approximation properties for linear combinations of moment type operators [J].

Bardaro, Carlo ;

Mantellini, Ilaria .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (05) :2304-2313

[10] A quantitative asymptotic formula for a general class of discrete operators [J].

Bardaro, Carlo ;

Mantellini, Ilaria .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 60 (10) :2859-2870

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