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The Poisson integrals of functions of two variables for Hermite and Laguerre expansions

Krech G.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2011

Vol. 16

47-54

In this paper we consider the Poisson integrals of functions of two variables for Hermite and Laguerre expansions in the spaces [wzór] and [wzór], respectively. We state some estimates of the rate of convergence of the Poisson integrals.

On composition operator in the algebra of functions of two variables with bounded total Φ-variation in Schramm sense

Ereu T., Merentes N., Rzepka B., Sanchez J. L.

Journal of Mathematics and Applications

2010

Vol. 33

35-50

In this paper we consider the so called composition operator being a self-mapping of the Banach algebra of the function of two variables with bounded total Φ-variation in the Schramm sense. The main result of the paper characterizes the composition operator mentioned above which has a generating function being Lipschitzian with respect to the second variable. The basic tool used in our considerations is the concept of the left-left regularization.

On some extremal problem of chosen two-parametrical families of real functions

Wrzesień A.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2008

Vol. 7, nr 2

97-105

In this paper we continue the investigation from [1]. There we have considered the case of the circle and the ellipse. Now we will take two-parametrical families of differentiable functions. For these families we determine extremality coefficients. In the last part of this paper we study the case of functions of two variables.