This article is cited in 2 papers

On Carleman–Vekua Equations with Nonfinitely Supported Coefficients on a Noncompact Riemann Surface

I. A. Bikchantaev

Kazan State University

Abstract: In this paper, we study equations of the form $\partial f+Af+B\bar f=G$, on an arbitrary noncompact Riemann surface $R$, where $A$, $B$, and $G$ are given square-integrable linear differentials of genus $(0,1)$ satisfying certain additional conditions. Necessary and sufficient conditions for the solvability of the above equation are proved for the class of functions with $\Lambda_0$-behavior in the neighborhood of the ideal boundary of the surface $R$; the index of the equation is also calculated.

UDC: 517.968.25+517.54

Received: 08.07.2002

DOI: 10.4213/mzm1

 English version: Mathematical Notes, 2004, 75:1, 3–12

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