Abstract: 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.
Keywords: continuous linear right inverse, differential operator of infinite order, space of germs of analytic functions, convex set
For citation: Barkina U. V., Melikhov S. N. On a solution operator for differential equations of infinity order on convex sets // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 4, pp. 27-40. DOI 10.23671/VNC.2014.4.10256
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