Geometric and approximation properties of generalized singular integrals in the unit disk. (English) Zbl 1107.30029

Anastassiou, George A.; Gal, Sorin G.

J. Korean Math. Soc. 43, No. 2, 425-443 (2006).

Consider \(f\) to be a (normalized) function in the disk algebra. The auhors prove estimates for the error of approximation of \(f\) by certain generalized complex singular integrals of Picard-, Poisson-Cauchy- and Gauss-Weierstrass-type. The results are in terms of the \((n+1)\)-st modulus of smoothness of \(f\). Also, approximation results for vector-valued functions on the unit disk are presented.

Reviewer: Jürgen Müller (Trier)

MSC:

30E10	Approximation in the complex plane
41A25	Rate of convergence, degree of approximation

Keywords:

Jackson-type estimates; complex singular integrals