Matematičeskie zametki, Tome 16 (1974) no. 3, pp. 415-422
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O. V. Epifanov. The problem concerning the epimorphicity of a convolution operator in convex domains. Matematičeskie zametki, Tome 16 (1974) no. 3, pp. 415-422. http://geodesic.mathdoc.fr/item/MZM_1974_16_3_a8/
@article{MZM_1974_16_3_a8,
author = {O. V. Epifanov},
title = {The problem concerning the epimorphicity of a~convolution operator in convex domains},
journal = {Matemati\v{c}eskie zametki},
pages = {415--422},
year = {1974},
volume = {16},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_3_a8/}
}
TY - JOUR
AU - O. V. Epifanov
TI - The problem concerning the epimorphicity of a convolution operator in convex domains
JO - Matematičeskie zametki
PY - 1974
SP - 415
EP - 422
VL - 16
IS - 3
UR - http://geodesic.mathdoc.fr/item/MZM_1974_16_3_a8/
LA - ru
ID - MZM_1974_16_3_a8
ER -
%0 Journal Article
%A O. V. Epifanov
%T The problem concerning the epimorphicity of a convolution operator in convex domains
%J Matematičeskie zametki
%D 1974
%P 415-422
%V 16
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1974_16_3_a8/
%G ru
%F MZM_1974_16_3_a8
We deduce an epimorphicity criterion for the convolution operator $$ (a*x)(z)=\frac1{2\pi i}\oint x(t)\tilde a(t-z)\,dt, $$ acting from a space of functions analytic in a convex domain into another such space; $\tilde a(z)$ is the Borel transformation of the exponential function $a(z)$.
