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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap79-3-1,
author = {George A. Anastassiou and Sorin G. Gal},
title = {On global smoothness preservation in complex approximation},
journal = {Annales Polonici Mathematici},
volume = {79},
year = {2002},
pages = {199-205},
zbl = {1013.30021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap79-3-1}
}
George A. Anastassiou; Sorin G. Gal. On global smoothness preservation in complex approximation. Annales Polonici Mathematici, Tome 79 (2002) pp. 199-205. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap79-3-1/