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

This article is cited in 5 scientific papers (total in 5 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.

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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
\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

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    This publication is cited in the following articles:
    1. O. A. Ivanova, S. N. Melikhov, “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  elib
    2. P. A. Ivanov, S. N. Melikhov, “Operator Pomme v prostranstvakh analiticheskikh funktsii mnogikh kompleksnykh peremennykh”, Kompleksnyi analiz, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 153, VINITI RAN, M., 2018, 55–68  mathnet  mathscinet
    3. O. A. Ivanova, S. N. Melikhov, “On Multiplication of Distributions Generated by the Pommiez Operator”, Math. Notes, 105:4 (2019), 625–629  mathnet  crossref  crossref  mathscinet  isi  elib
    4. 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  mathscinet
    5. O. A. Ivanova, S. N. Melikhov, “Algebry analiticheskikh funktsionalov i obobschennoe proizvedenie Dyuamelya”, Vladikavk. matem. zhurn., 22:3 (2020), 72–84  mathnet  crossref
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