RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Vladikavkaz. Mat. Zh.: Year: Volume: Issue: Page: Find

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

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)
References: PDF file   HTML file
UDC: 517.9

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} 

• http://mi.mathnet.ru/eng/vmj519
• http://mi.mathnet.ru/eng/vmj/v16/i4/p27

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. A. B. Shabat, “Difference Schrödinger equation and quasisymmetric polynomials”, Theoret. and Math. Phys., 184:2 (2015), 1067–1077
3. M. Sh. Badakhov, A. B. Shabat, “Darboux transformations in the inverse scattering problem”, Ufa Math. J., 8:4 (2016), 42–51
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
•  Number of views: This page: 199 Full text: 55 References: 33