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 Zap. Nauchn. Sem. POMI, 2016, Volume 447, Pages 90–112 (Mi znsl6296)

On generators of spaces of entire functions with a system of weighted estimates

D. A. Polyakovaab

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

Abstract: We consider spaces of entire functions with systems of weight estimates. The case of binomial weight sequences consisting of radial and nonradial components is investigated. Under some assumptions on the weight sequence we obtain a complete description of generators in these spaces. We apply this result to the problem of normal solvability of systems of convolution equations in the Roumieu spaces of ultradifferentiable functions and, as a particular case, in Gevrey classes.

Key words and phrases: entire functions, projective weighted spaces, generators, systems of convolution equations.

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English version:
Journal of Mathematical Sciences (New York), 2018, 229:5, 545–560

Bibliographic databases:

UDC: 517.5

Citation: D. A. Polyakova, “On generators of spaces of entire functions with a system of weighted estimates”, Investigations on linear operators and function theory. Part 44, Zap. Nauchn. Sem. POMI, 447, POMI, St. Petersburg, 2016, 90–112; J. Math. Sci. (N. Y.), 229:5 (2018), 545–560

Citation in format AMSBIB
\Bibitem{Pol16} \by D.~A.~Polyakova \paper On generators of spaces of entire functions with a system of weighted estimates \inbook Investigations on linear operators and function theory. Part~44 \serial Zap. Nauchn. Sem. POMI \yr 2016 \vol 447 \pages 90--112 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6296} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3580164} \transl \jour J. Math. Sci. (N. Y.) \yr 2018 \vol 229 \issue 5 \pages 545--560 \crossref{https://doi.org/10.1007/s10958-018-3697-0} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85041546275}