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DOI: 10.23671/VNC.2016.4.5989

On an Algebra of Analytic Functionals Connected with a Pommiez Operator

Ivanova, O. A. , Melikhov, S. N.
Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 4.
We study properties of a convolution algebra formed by the dual\(E'\) of a countable inductive limit \(E\) of weighted  Frechet 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 \((E',\otimes)\).
Keywords: weighted space of entire functions, algebra of analytic functionals, Pommiez operator, commutant
Language: Russian Download the full text  
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