Zolota O. The asymptotic properties of analytic and harmonic functions in the polydisc represented by the Poisson-Stieltjes integrals

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0412U006409

Thesis Registration Form

0412U006409.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

22-11-2012

Specialized Academic Board

Д 35.051.18

Ivan Franko National University of Lviv

Essay

In the paper the Poisson-Stieltjes integral of the complex-valued Borel measure on the skeleton is considered. In terms of the smoothness of Stieltjes measure the necessary conditions and sufficient conditions of the growth of these integrals and their generalizations are obtained. Besides, the asymptotic behavior of analytic functions, represented by Cauchy-Stieltjes integrals, when the arguments tend to points of the skeleton outside the exceptional sets, is investigated. Sharp estimates of the exceptional sets are obtained.

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