General uniform approximation theory by multivariate singular integral operators

George A. Anastassiou

Annales Polonici Mathematici (2012)

  • Volume: 103, Issue: 1, page 15-25
  • ISSN: 0066-2216

Abstract

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We study the uniform approximation properties of general multivariate singular integral operators on ℝ N , N ≥ 1. We establish their convergence to the unit operator with rates. The estimates are pointwise and uniform. The established inequalities involve the multivariate higher order modulus of smoothness. We list the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators to which this theory can be applied directly.

How to cite

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George A. Anastassiou. "General uniform approximation theory by multivariate singular integral operators." Annales Polonici Mathematici 103.1 (2012): 15-25. <http://eudml.org/doc/280344>.

@article{GeorgeA2012,
abstract = {We study the uniform approximation properties of general multivariate singular integral operators on $ℝ^\{N\}$, N ≥ 1. We establish their convergence to the unit operator with rates. The estimates are pointwise and uniform. The established inequalities involve the multivariate higher order modulus of smoothness. We list the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators to which this theory can be applied directly.},
author = {George A. Anastassiou},
journal = {Annales Polonici Mathematici},
keywords = {multivariate singular integral operator; multivariate modulus of smoothness; rate of convergence; multivariate Picard; Gauss-Weierstrass; Poisson-Cauchy and trigonometric singular integral operators},
language = {eng},
number = {1},
pages = {15-25},
title = {General uniform approximation theory by multivariate singular integral operators},
url = {http://eudml.org/doc/280344},
volume = {103},
year = {2012},
}

TY - JOUR
AU - George A. Anastassiou
TI - General uniform approximation theory by multivariate singular integral operators
JO - Annales Polonici Mathematici
PY - 2012
VL - 103
IS - 1
SP - 15
EP - 25
AB - We study the uniform approximation properties of general multivariate singular integral operators on $ℝ^{N}$, N ≥ 1. We establish their convergence to the unit operator with rates. The estimates are pointwise and uniform. The established inequalities involve the multivariate higher order modulus of smoothness. We list the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators to which this theory can be applied directly.
LA - eng
KW - multivariate singular integral operator; multivariate modulus of smoothness; rate of convergence; multivariate Picard; Gauss-Weierstrass; Poisson-Cauchy and trigonometric singular integral operators
UR - http://eudml.org/doc/280344
ER -

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