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., 2016, Volume 18, Number 4, Pages 34–40 (Mi vmj595)

On an algebra of analytic functionals connected with a Pommiez operator

O. A. Ivanovaa, S. N. Melikhovab

a Southern Federal University, Rostov-on-Don
b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences

Abstract: We study properties of a convolution algebra formed by the dual $E'$ of a countable inductive limit $E$ of weighted Fréchet spaces of entire funtions of one complex variable with the multiplication-convolution $\otimes$ which is defined with the help of the shift operator for a Pommiez operator. The algebra $(E',\otimes)$ is isomorphic to the commutant of a Pommiez operator in the ring of all continuous linear operators in $E$. We prove that this isomorphism is topological if $E'$ is endowed with the weak topology and the corresponding commutant is endowed with the weakly operator topology. This result we use for powers of a Pommiez operator series expansions for all continuous linear operators commuting with this Pommiez operator on $E$. We describe also all nonzero multiplicative functionals on the algebra $(E',\otimes)$.

Key words: weighted space of entire functions, algebra of analytic functionals, Pommiez operator, commutant.

Full text: PDF file (219 kB)
References: PDF file   HTML file
UDC: 517.9

Citation: O. A. Ivanova, S. N. Melikhov, “On an algebra of analytic functionals connected with a Pommiez operator”, Vladikavkaz. Mat. Zh., 18:4 (2016), 34–40

Citation in format AMSBIB
\Bibitem{IvaMel16} \by O.~A.~Ivanova, S.~N.~Melikhov \paper On an algebra of analytic functionals connected with a Pommiez operator \jour Vladikavkaz. Mat. Zh. \yr 2016 \vol 18 \issue 4 \pages 34--40 \mathnet{http://mi.mathnet.ru/vmj595} 

• http://mi.mathnet.ru/eng/vmj595
• http://mi.mathnet.ru/eng/vmj/v18/i4/p34

 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. S. N. Melikhov, O. A. Ivanova, “Kommutant operatora Pomme v prostranstve tselykh funktsii eksponentsialnogo tipa i polinomialnogo rosta na veschestvennoi pryamoi”, Vladikavk. matem. zhurn., 20:3 (2018), 48–56
2. O. A. Ivanova, S. N. Melikhov, “Ob umnozhenii raspredelenii, porozhdaemom operatorom Pomme”, Matem. zametki, 105:4 (2019), 632–636
3. S. N. Melikhov, “Koeffitsienty ryadov eksponent dlya analiticheskikh funktsii i operator Pomme”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 65–103
•  Number of views: This page: 121 Full text: 35 References: 18