Abstract:
This paper describes some classes of entire functions of finite order that admit natural estimates outside a system of pairwise disjoint disks with centers at the zeros. The Hermite interpolation problem is solved under weaker conditions than were previously used, for the class of functions of finite type and for classes of functions with indicator not exceeding a given one. In a number of spaces of holomorphic functions we describe, completely or partially, the invariant subspaces in which the root vectors of the differentiation operator form a basis.
Bibliography: 41 titles.
Citation:
A. V. Bratishchev, “A type of lower estimate for entire functions of finite order, and some applications”, Math. USSR-Izv., 24:3 (1985), 415–438
\Bibitem{Bra84}
\by A.~V.~Bratishchev
\paper A~type of lower estimate for entire functions of finite order, and some applications
\jour Math. USSR-Izv.
\yr 1985
\vol 24
\issue 3
\pages 415--438
\mathnet{http://mi.mathnet.ru/eng/im1453}
\crossref{https://doi.org/10.1070/IM1985v024n03ABEH001243}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=747248}
\zmath{https://zbmath.org/?q=an:0565.30021|0551.30026}
Linking options:
https://www.mathnet.ru/eng/im1453
https://doi.org/10.1070/IM1985v024n03ABEH001243
https://www.mathnet.ru/eng/im/v48/i3/p451
This publication is cited in the following 8 articles:
V. B. Sherstyukov, “Asymptotic properties of entire functions with given laws of distribution of zeros”, J. Math. Sci. (N. Y.), 257:2 (2021), 246–272
K. G. Malyutin, “Interpolation Problems of A. F. Leontiev Type”, J. Math. Sci. (N. Y.), 252:3 (2021), 399–419
G. G. Braichev, V. B. Sherstyukov, “Sharp bounds for asymptotic characteristics of growth of entire functions with zeros on given sets”, J. Math. Sci., 250:3 (2020), 419–453
V. B. Sherstyukov, “K probleme Leonteva o tselykh funktsiyakh vpolne regulyarnogo rosta”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 13:2(1) (2013), 30–35
V. B. Sherstyukov, “On Some Criteria
for Completely Regular Growth
of Entire Functions of Exponential Type”, Math. Notes, 80:1 (2006), 114–126
V. V. Napalkov, V. E. Kim, “Isomorphism between the solution spaces of a discrete convolution equation and a convolution equation on the space of entire functions”, Math. Notes, 80:5 (2006), 692–709
A. S. Krivosheev, “A fundamental principle for invariant subspaces in convex domains”, Izv. Math., 68:2 (2004), 291–353
A. S. Krivosheev, “Interpolation with estimates in Cn and its applications”, Sb. Math., 192:9 (2001), 1297–1340
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