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On global smoothness preservation in complex approximation

George A. Anastassiou, Sorin G. Gal (2002)

Annales Polonici Mathematici

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.

On some shift invariant integral operators, univariate case

George A. Anastassiou, Heinz H. Gonska (1995)

Annales Polonici Mathematici

In recent papers the authors studied global smoothness preservation by certain univariate and multivariate linear operators over compact domains. Here the domain is ℝ. A very general positive linear integral type operator is introduced through a convolution-like iteration of another general positive linear operator with a scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates, shape preserving and...

Open problems in constructive function theory.

Baratchart, L., Martínez-Finkelshtein, A., Jimenez, D., Lubinsky, D.S., Mhaskar, H.N., Pritsker, I., Putinar, M., Stylianopoulos, N., Totik, V., Varju, P., Xu, Y. (2006)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Uniform approximation with linear combinations of reproducing kernels

Jan Mycielski, Stanisław Świerczkowski (1996)

Studia Mathematica

We show several theorems on uniform approximation of functions. Each of them is based on the choice of a special reproducing kernel in an appropriate Hilbert space. The theorems have a common generalization whose proof is founded on the idea of the Kaczmarz projection algorithm.

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