Azarin limit sets of some irregularly growing functions

Author(s):  K.G. Malyutin, Dr., Prof., Southwest State University, Kursk, Russia, malyutinkg@gmail.com

L.I. Studenikina, candidate of Sciences, associate Professor, Southwest State University, Kursk, Russia, sli-kursk@yandex.ru

D.N. Tutunov, candidate of Sciences, associate Professor, Southwest State University, Kursk, Russia, tjutjunov@mail.ru

T.V. Shevtsova, Southwest State University, Kursk, Russia, dec-ivt-zao@mail.ru

Issue:  Volume 50, №1

Rubric:  Mathematics

Annotation:  A method of constructing asymptotic formulas for integrals with an absolutely continuous function is considered. It are considered cases when as an absolutely continuous function is taken the product of a power function on the conjugate Poisson kernel for a half-plane, and as a gap, the imaginary half-axis is taken. The real and imaginary parts of these integrals are harmonic functions in the complex plane cut along a positive ray. For such functions the Azarin limit set is calculated

Keywords:  asymptotic formula, conjugate Poisson kernel, harmonic function, Azarin limit set

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