Ukrainian Mathematical Journal

, Volume 58, Issue 4, pp 596–618 | Cite as

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

  • V. V. Savchuk


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.


Lebesgue Measure Holomorphic Function Borel Measure Weak Topology Multidimensional Case 
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© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. V. Savchuk
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKyiv

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