TY - JOUR
T1 - Generalized analytic functions of several variables
AU - Magomedov, G. A.
AU - Palamodov, V. P.
PY - 1979/2/28
Y1 - 1979/2/28
N2 - In this paper the system of differential equations is studied in a domain in. Differential relations between the coefficients are indicated under which the homogeneous system 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 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.
AB - In this paper the system of differential equations is studied in a domain in. Differential relations between the coefficients are indicated under which the homogeneous system 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 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.
UR - http://www.scopus.com/inward/record.url?scp=0040963640&partnerID=8YFLogxK
U2 - 10.1070/SM1979v035n02ABEH001464
DO - 10.1070/SM1979v035n02ABEH001464
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0040963640
SN - 0025-5734
VL - 35
SP - 181
EP - 205
JO - Mathematics of the USSR - Sbornik
JF - Mathematics of the USSR - Sbornik
IS - 2
ER -