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Journal of Mathematical Sciences

, Volume 237, Issue 1, pp 30–109 | Cite as

Singular Generalized Analytic Functions

  • G. GiorgadzeEmail author
  • V. Jikia
  • G. Makatsaria
Article
  • 5 Downloads

Abstract

In this paper, we consider solution spaces for some class of singular elliptic systems on Riemann surfaces and boundary-value problems for solution spaces of such systems. We also discuss some relations for the kernels of the Carleman–Vekua equation. In particular, representations of these kernels in the form of generalized power functions are completely analogous to the classical Cauchy kernel expansion. The obtained results are applied to some problems of the theory of generalized analytic functions.

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Authors and Affiliations

  1. 1.Iv. Javakhishvili Tbilisi State UniversityTbilisiGeorgia
  2. 2.I. Vekua Institute of Applied MathematicsTbilisi State UniversityTbilisiGeorgia
  3. 3.Saint Andrew The First-Called Georgian University of Patriarchate of GeorgiaTbilisiGeorgia

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