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Mat. Sb. (N.S.), 1978, Volume 106(148), Number 4(8), Pages 515–543 (Mi msb2604)  

This article is cited in 7 scientific papers (total in 7 papers)

Generalized analytic functions of several variables

G. A. Magomedov, V. P. Palamodov


Abstract: In this paper the system of differential equations
$$ \frac{\partial u}{\partial\bar z_k}-\overline{a_ku}=f_k,\qquad k=1,2,…,n $$
is studied in a domain in $\mathbf C^n$. Differential relations between the coefficients are indicated under which the homogeneous system ($f_k=0$) has infinitely many linearly independent local solutions at each point. Global solvability of the system is studied. It is proved that this problem, and also the description of global solutions of the homogeneous system, reduces to analogous questions for a connection of the type $\partial u/\partial\bar z=\overline{au}+bu$ in a line bundle over a Riemann surface, related to the original system in a natural way. Using this reduction, in some cases one can establish that the index of the operator corresponding to this system is finite and find a formula for it.
Bibliography: 11 titles.

Full text: PDF file (2802 kB)
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English version:
Mathematics of the USSR-Sbornik, 1979, 35:2, 181–205

Bibliographic databases:

UDC: 517.945.7+517.551
MSC: 30G20, 32A30
Received: 27.10.1977

Citation: G. A. Magomedov, V. P. Palamodov, “Generalized analytic functions of several variables”, Mat. Sb. (N.S.), 106(148):4(8) (1978), 515–543; Math. USSR-Sb., 35:2 (1979), 181–205

Citation in format AMSBIB
\Bibitem{MagPal78}
\by G.~A.~Magomedov, V.~P.~Palamodov
\paper Generalized analytic functions of several variables
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 106(148)
\issue 4(8)
\pages 515--543
\mathnet{http://mi.mathnet.ru/msb2604}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=507814}
\zmath{https://zbmath.org/?q=an:0421.35062|0382.35039}
\transl
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 2
\pages 181--205
\crossref{https://doi.org/10.1070/SM1979v035n02ABEH001464}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JB17600003}


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  • http://mi.mathnet.ru/eng/msb/v148/i4/p515

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Tutschke W., “Analyticity of the Set of All Zeros of Solutions for Implicit Non-Linear Systems of Partial-Differential Equations”, Math. Nachr., 101 (1981), 27–35  crossref  mathscinet  zmath  isi
    2. Magomedov G., “The Theory of Generalized Analytic Vector of Many Variables”, 273, no. 2, 1983, 289–292  mathscinet  zmath  isi
    3. Koohara A., “Function-Theoretic Properties of Solutions of Semi-Linear Deltabar-Equations - Similarity Principle”, Osaka J. Math., 24:4 (1987), 817–852  mathscinet  zmath  isi
    4. Dzhurayev A., “On One Overdetermined 1st-Order Elliptic System”, 320, no. 6, 1991, 1300–1304  isi
    5. Yasuo Hayashi, “Compatibility Conditions and the Manifold of Solutions of some Nonlinear Cauchy-Riemann System in Several Complex Variables”, Math Nachr, 159:1 (1992), 153  crossref  mathscinet  zmath  isi
    6. Yasuo Hayashi, “A Global Theory of Some Nonlinear Cauchy-Riemann System in Several Complex Variables”, Math Nachr, 178:1 (1996), 157  crossref  mathscinet  zmath  isi
    7. Z. G. Medzhidov, “$L_2$-estimates and existence theorems for generalized analytic functions in several variables”, Siberian Math. J., 45:4 (2004), 699–708  mathnet  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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