Geodesic
On a~solution operator for differential equations of infinity order on convex sets
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 4, pp. 27-40

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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. 
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     author = {U. V. Barkina and S. N. Melikhov},
     title = {On a~solution operator for differential equations of infinity order on convex sets},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
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U. V. Barkina; S. N. Melikhov. On a~solution operator for differential equations of infinity order on convex sets. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 4, pp. 27-40. http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a3/