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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 4, pp. 522–542, April, 2006.
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Savchuk, V.V. Representation of holomorphic functions of many variables by Cauchy-Stieltjes-type integrals. Ukr Math J 58, 596–618 (2006). https://doi.org/10.1007/s11253-006-0086-5
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DOI: https://doi.org/10.1007/s11253-006-0086-5