Singular Generalized Analytic Functions

Аннотация

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.