Geodesic
Vekua Integral Operators on Riemann Surfaces
Matematičeskie zametki, Tome 69 (2001) no. 1, pp. 18-30 Cet article a éte moissonné depuis la source Math-Net.Ru

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On an arbitrary (in general, noncompact) Riemann surface $R$, we study integral operators $\operatorname{T}$ and $\Pi$ analogous to the operators introduced by Vekua in his theory of generalized analytic functions. By way of application, we obtain necessary and sufficient conditions for the solvability of the nonhomogeneous Cauchy–Riemann equation $\overline\partial f=F$ in the class of functions $f$ exhibiting $\Lambda_0$-behavior in the vicinity of the ideal boundary of $R$. 
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     author = {I. A. Bikchantaev},
     title = {Vekua {Integral} {Operators} on {Riemann} {Surfaces}},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a1/}
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I. A. Bikchantaev. Vekua Integral Operators on Riemann Surfaces. Matematičeskie zametki, Tome 69 (2001) no. 1, pp. 18-30. http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a1/

[1] Forster O., Rimanovy poverkhnosti, Mir, M., 1980

[2] Vekua I. N., Obobschennye analiticheskie funktsii, Nauka, M., 1988 | Zbl

[3] Shiba M., “On the Riemann–Roch theorem on open Riemann surfaces”, J. Math. Kyoto Univ., 11:3 (1971), 495–525 | MR | Zbl

[4] Shiba M., “Some general properties of behavior spaces of harmonic semiexact differentials on an open Riemann surface”, Hiroshima Math. J., 8:1 (1978), 151–164 | MR | Zbl

[5] Bikchantaev I. A., “Integralnye predstavleniya reshenii ellipticheskikh sistem pervogo poryadka na rimanovykh poverkhnostyakh”, Differents. uravneniya, 22:9 (1986), 1557–1565 | MR | Zbl

[6] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1976

[7] Bikchantaev I. A., “Analogi yadra Koshi na rimanovoi poverkhnosti i nekotorye ikh prilozheniya”, Matem. sb., 112:2 (1980), 256–282 | MR | Zbl