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Mat. Zametki, 2001, Volume 69, Issue 1, Pages 18–30 (Mi mz480)  

This article is cited in 4 scientific papers (total in 4 papers)

Vekua Integral Operators on Riemann Surfaces

I. A. Bikchantaev

Kazan State University

Abstract: 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 $R$.

DOI: https://doi.org/10.4213/mzm480

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English version:
Mathematical Notes, 2001, 69:1, 17–27

Bibliographic databases:

UDC: 517.968.25+517.54
Received: 04.02.2000

Citation: I. A. Bikchantaev, “Vekua Integral Operators on Riemann Surfaces”, Mat. Zametki, 69:1 (2001), 18–30; Math. Notes, 69:1 (2001), 17–27

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. A. Barieva, I. A. Bikchantaev, “A conjugation problem for the nonhomogeneous Cauchy–Riemann equation on a Riemann surface”, Russian Math. (Iz. VUZ), 46:8 (2002), 6–10  mathnet  mathscinet  elib
    2. I. A. Bikchantaev, “On Carleman–Vekua Equations with Nonfinitely Supported Coefficients on a Noncompact Riemann Surface”, Math. Notes, 75:1 (2004), 3–12  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. I. A. Bikchantaev, “The Hilbert problem for a first-order linear elliptic system with noncompactly supported coefficients on a Riemann surface with a boundary”, Russian Math. (Iz. VUZ), 50:1 (2006), 14–22  mathnet  mathscinet  zmath  elib
    4. Bikchantaev, IA, “The R-linear conjugation problem for the Carleman-Vekua equation on an open Riemann surface”, Differential Equations, 43:2 (2007), 280  crossref  mathscinet  zmath  isi  elib  scopus
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