On some properties of generalized analytic functions induced from irregular Carleman–Bers–Vekua equations

Abstract

In this article we study solution spaces of Carleman–Bers–Vekua equations with coefficients from the space , p > 2. In particular, we investigate such solutions which satisfy certain additional asymptotic conditions and calculate the dimensions of corresponding subspaces of these solution spaces.

Keywords:

• irregular Carleman–Bers–Vekua equation
• Liouville-type theorem
• generalized analytic function
• pseudoanalytic function

AMS Subject Classification:

• 30G20

Acknowledgements

The authors are grateful to the participants of the seminar ‘Elliptic systems on Riemann surfaces’ at the Tbilisi State University for many discussions. This article was partially supported by the Rustaveli Foundation, Grant No 1-3/85