2017
Том 69
№ 6

All Issues

Representation of holomorphic functions of many variables by Cauchy-Stieltjes-type integrals

Savchuk V. V.

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Abstract

We consider functions of many complex variables that are holomorphic in a polydisk or in the upper half-plane. We give necessary and sufficient conditions under which a holomorphic function is a Cauchy-Stieltjes-type integral of a complex charge. We present several applications of this criterion to integral representations of certain classes of holomorphic functions.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 4, pp 596-618.

Citation Example: Savchuk V. V. Representation of holomorphic functions of many variables by Cauchy-Stieltjes-type integrals // Ukr. Mat. Zh. - 2006. - 58, № 4. - pp. 522–542.

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