On global smoothness preservation in complex approximation

George A. Anastassiou; Sorin G. Gal

Annales Polonici Mathematici (2002)

  • Volume: 79, Issue: 3, page 199-205
  • ISSN: 0066-2216

Abstract

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By using the properties of convergence and global smoothness preservation of multivariate Weierstrass singular integrals, we establish multivariate complex Carleman type approximation results with rates. Here the approximants fulfill the global smoothness preservation property. Furthermore Mergelyan's theorem for the unit disc is strengthened by proving the global smoothness preservation property.

How to cite

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George A. Anastassiou, and Sorin G. Gal. "On global smoothness preservation in complex approximation." Annales Polonici Mathematici 79.3 (2002): 199-205. <http://eudml.org/doc/281012>.

@article{GeorgeA2002,
abstract = {By using the properties of convergence and global smoothness preservation of multivariate Weierstrass singular integrals, we establish multivariate complex Carleman type approximation results with rates. Here the approximants fulfill the global smoothness preservation property. Furthermore Mergelyan's theorem for the unit disc is strengthened by proving the global smoothness preservation property.},
author = {George A. Anastassiou, Sorin G. Gal},
journal = {Annales Polonici Mathematici},
keywords = {global smoothness preservation property; moduli of smoothness; multivariate Weierstrass singular integral; multivariate complex Carleman type approximation result; entire function; Mergelyan type results; Fejér kernel},
language = {eng},
number = {3},
pages = {199-205},
title = {On global smoothness preservation in complex approximation},
url = {http://eudml.org/doc/281012},
volume = {79},
year = {2002},
}

TY - JOUR
AU - George A. Anastassiou
AU - Sorin G. Gal
TI - On global smoothness preservation in complex approximation
JO - Annales Polonici Mathematici
PY - 2002
VL - 79
IS - 3
SP - 199
EP - 205
AB - By using the properties of convergence and global smoothness preservation of multivariate Weierstrass singular integrals, we establish multivariate complex Carleman type approximation results with rates. Here the approximants fulfill the global smoothness preservation property. Furthermore Mergelyan's theorem for the unit disc is strengthened by proving the global smoothness preservation property.
LA - eng
KW - global smoothness preservation property; moduli of smoothness; multivariate Weierstrass singular integral; multivariate complex Carleman type approximation result; entire function; Mergelyan type results; Fejér kernel
UR - http://eudml.org/doc/281012
ER -

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