The Picard and the Gauss-Weierstrass singular integrals of functions in two variables
Keywords:
Picard singular integral, Gauss-Weierstrasse singular integral, Degree of approximation, Voronovskaya theoremAbstract
We study some approximation properties of the Picard and the Gauss-Weierstrass singular integrals of functions of two variables belonging to some exponential weighted spaces. In Sec. 3.1 and 3.2 we give two theorems on the degree of approximation and two theorems of the Voronovskaya type. In Sec. 3.3 the Bernstein inequalities for these singular integrals are proved.
Some similar results for the Picard and the Gauss-Weierstrass singular integral of functions of one variable were given in [1] - [3].
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