Geodesic
Convolution equations in the complex domain
Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 171-194

Voir la notice de l'article provenant de la source Math-Net.Ru

This article investigates analytic solutions of a convolution equation and of systems of two convolution equations with a single unknown function. The characteristic functions of all the convolution operators studied here are entire functions of exponential type. A general representation is determined for solutions of homogeneous and inhomogeneous equations and of systems of such equations in the form of absolutely convergent series in entire functions (as a rule, exponentials forming an absolutely representing system). A criterion is established for solvability of a system of two inhomogeneous convolution equations with a single unknown function. The main results are obtained with the help of nontrivial expansions of zero in convex domains with respect to functions forming an absolutely representing system. Bibliography: 19 titles. 
@article{SM_1986_55_1_a10,
     author = {Yu. F. Korobeinik},
     title = {Convolution equations in the complex domain},
     journal = {Sbornik. Mathematics},
     pages = {171--194},
     publisher = {mathdoc},
     volume = {55},
     number = {1},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1986_55_1_a10/}
}
TY  - JOUR
AU  - Yu. F. Korobeinik
TI  - Convolution equations in the complex domain
JO  - Sbornik. Mathematics
PY  - 1986
SP  - 171
EP  - 194
VL  - 55
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1986_55_1_a10/
LA  - en
ID  - SM_1986_55_1_a10
ER  - 
%0 Journal Article
%A Yu. F. Korobeinik
%T Convolution equations in the complex domain
%J Sbornik. Mathematics
%D 1986
%P 171-194
%V 55
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1986_55_1_a10/
%G en
%F SM_1986_55_1_a10
Yu. F. Korobeinik. Convolution equations in the complex domain. Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 171-194. http://geodesic.mathdoc.fr/item/SM_1986_55_1_a10/