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Vladikavkaz. Mat. Zh., 2014, Volume 16, Number 4, Pages 27–40 (Mi vmj519)  

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

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.

Key words: continuous linear right inverse, differential operator of infinite order, space of germs of analytic functions, convex set.

Full text: PDF file (293 kB)
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UDC: 517.9
Received: 11.08.2014

Citation: 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
\Bibitem{BarMel14}
\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.
\yr 2014
\vol 16
\issue 4
\pages 27--40
\mathnet{http://mi.mathnet.ru/vmj519}


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    This publication is cited in the following articles:
    1. A. B. Shabat, “Scattering theory for delta-type potentials”, Theoret. and Math. Phys., 183:1 (2015), 540–552  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. B. Shabat, “Difference Schrödinger equation and quasisymmetric polynomials”, Theoret. and Math. Phys., 184:2 (2015), 1067–1077  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. M. Sh. Badakhov, A. B. Shabat, “Darboux transformations in the inverse scattering problem”, Ufa Math. J., 8:4 (2016), 42–51  mathnet  crossref  isi  elib
    4. S. N. Melikhov, L. V. Khanina, “Analytic solutions of convolution equations on convex sets in the complex plane with an open obstacle on the boundary”, Sb. Math., 211:7 (2020), 1014–1040  mathnet  crossref  crossref  isi
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