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

This article is cited in 3 scientific papers (total in 3 papers)

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)
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UDC: 517.9
Received: 12.08.2016

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}


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    Citing articles on Google Scholar: Russian citations, English citations
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    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  mathnet  crossref
    2. O. A. Ivanova, S. N. Melikhov, “Ob umnozhenii raspredelenii, porozhdaemom operatorom Pomme”, Matem. zametki, 105:4 (2019), 632–636  mathnet  crossref  elib
    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  mathnet
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