This article is cited in 4 scientific papers (total in 4 papers)
On a solution operator for differential equations of infinity order on convex sets
U. V. Barkinaa, S. N. Melikhovab
a Southern Federal University, Rostov-on-Don, Russia
b South Mathematical Institute of VSC RAS, Vladikavkaz, Russia
Let $Q$ be a convex (not necessarily bounded) set in $\mathbb C$ with the nonempty interior which has a countable neighborhood base of convex domains; $A(Q)$ be the space of germs of all analytic functions on $Q$ with its natural inductive limit topology. Necessary and sufficient conditions under which a fixed nonzero differential operator of infinite order with constant coefficients which acts in $A(Q)$ has a continuous linear right inverse are established. This criterion is obtained in terms of the existence of a special family of subharmonic functions.
continuous linear right inverse, differential operator of infinite order, space of germs of analytic functions, convex set.
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U. V. Barkina, S. N. Melikhov, “On a solution operator for differential equations of infinity order on convex sets”, Vladikavkaz. Mat. Zh., 16:4 (2014), 27–40
Citation in format AMSBIB
\by U.~V.~Barkina, S.~N.~Melikhov
\paper On a~solution operator for differential equations of infinity order on convex sets
\jour Vladikavkaz. Mat. Zh.
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