General theory of global smoothness and approximation by smooth singular operators

被引：0

作者：

Anastassiou, George A. ^{[1
]}

Mezei, Razvan A. ^{[1
]}

机构：

[1] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA

来源：

MATHEMATICAL AND COMPUTER MODELLING | 2011年 / 54卷 / 1-2期

关键词：

Simultaneous approximation with rates; General singular integral; Trigonometric singular integral; Modulus of smoothness; UNIFORM-CONVERGENCE; INTEGRALS; RATES;

D O I：

10.1016/j.mcm.2011.02.019

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this article we continue with the study of smooth general singular integral operators over the real line regarding their simultaneous global smoothness preservation property with respect to the L-p norm, 1 <= p <= infinity, by involving higher order moduli of smoothness. Also we study their simultaneous approximation to the unit operator with rates involving the modulus of smoothness. The produced Jackson type inequalities are almost sharp containing elegant constants, and they reflect the high order of differentiability of the engaged function. We finish with applications to trigonometric singular integral operators. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：344 / 358

页数：15

共 50 条

[1] General theory of global smoothness and approximation by smooth singular operators
Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, United States
Math. Comput. Model., 1-2 (344-358):
[2] Global smoothness preservation and simultaneous approximation for multivariate general singular integral operators
Anastassiou, George A.
APPLIED MATHEMATICS LETTERS, 2011, 24 (06) : 1009 - 1016
[3] Global smoothness and uniform convergence of smooth Picard singular operators
Anastassiou, GA
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 50 (10-12) : 1755 - 1766
[4] Quantitative approximation by fractional smooth general singular operators
Anastassiou, George A.
Mezei, Razvan A.
APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (11) : 6200 - 6213
[5] Global smoothness and uniform convergence of smooth Gauss-Weierstrass singular operators
Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, United States
Math. Comput. Model., 1600, 7-8 (984-998):
[6] Global smoothness and uniform convergence of smooth Gauss-Weierstrass singular operators
Anastassiou, George A.
Mezei, Razvan A.
MATHEMATICAL AND COMPUTER MODELLING, 2009, 50 (7-8) : 984 - 998
[7] Global smoothness and uniform convergence of smooth Poisson-Cauchy type singular operators
Anastassiou, George A.
Mezei, Razvan A.
APPLIED MATHEMATICS AND COMPUTATION, 2009, 215 (05) : 1718 - 1731
[8] General uniform approximation theory by multivariate singular integral operators
Anastassiou, George A.
ANNALES POLONICI MATHEMATICI, 2012, 103 (01) : 15 - 25
[9] Global smoothness preservation and simultaneous approximation by multivariate discrete operators
Anastassiou, George A.
Kester, Merve
STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2016, 61 (03): : 257 - 278
[10] A direct theorem of approximation theory for a general modulus of smoothness
K. V. Runovski
Mathematical Notes, 2014, 95 : 833 - 842

← 1 2 3 4 5 →