Geodesic
On Carleman--Vekua Equations with Nonfinitely Supported Coefficients on a Noncompact Riemann Surface
Matematičeskie zametki, Tome 75 (2004) no. 1, pp. 3-12

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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. 
@article{MZM_2004_75_1_a0,
     author = {I. A. Bikchantaev},
     title = {On {Carleman--Vekua} {Equations} with {Nonfinitely} {Supported} {Coefficients} on a {Noncompact} {Riemann} {Surface}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {3--12},
     publisher = {mathdoc},
     volume = {75},
     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_1_a0/}
}
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I. A. Bikchantaev. On Carleman--Vekua Equations with Nonfinitely Supported Coefficients on a Noncompact Riemann Surface. Matematičeskie zametki, Tome 75 (2004) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/MZM_2004_75_1_a0/