Abstract:
This article contains a study of weakly sufficient sets in a certain space of entire functions of exponential type. The following is a consequence of the results obtained: If $D$ is an infinite convex domain, then there exists a system $\{\lambda_k\}_{k=1}^\infty$ (which is minimal in a certain sense) such that any analytic function in $D$ can be represented by a series of the form $\sum a_k\exp\lambda_kz$. For bounded convex domains an analogous result was obtained previously by Leont'ev.
Bibliography: 10 titles.
\Bibitem{Nap81}
\by V.~V.~Napalkov
\paper On~discrete weakly sufficient sets in certain spaces of entire functions
\jour Math. USSR-Izv.
\yr 1982
\vol 19
\issue 2
\pages 349--357
\mathnet{http://mi.mathnet.ru/eng/im1599}
\crossref{https://doi.org/10.1070/IM1982v019n02ABEH001421}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=637617}
\zmath{https://zbmath.org/?q=an:0499.30008|0481.30042}
Linking options:
https://www.mathnet.ru/eng/im1599
https://doi.org/10.1070/IM1982v019n02ABEH001421
https://www.mathnet.ru/eng/im/v45/i5/p1088
This publication is cited in the following 10 articles:
R. A. Bashmakov, K. P. Isaev, R. S. Yulmukhametov, “Representing Systems of Exponentials in Weight Subspaces $H(D)$”, J. Math. Sci. (N. Y.), 252:3 (2021), 302–318
K. P. Isaev, K. V. Trounov, R. S. Yulmukhametov, “Representation of functions in locally convex subspaces of $A^\infty (D)$ by series of exponentials”, Ufa Math. J., 9:3 (2017), 48–60
A. V. Abanin, V. A. Varziev, “Sufficient sets in weighted Fréchet spaces of entire functions”, Siberian Math. J., 54:4 (2013), 575–587
V. V. Napalkov, A. A. Nuyatov, “The multipoint de la Vallée-Poussin problem for a convolution operator”, Sb. Math., 203:2 (2012), 224–233
Nuyatov A.A., “Usloviya razreshimosti mnogotochechnoi zadachi valle pussena dlya operatorov svertki”, Vestnik nizhegorodskogo universiteta im. N.I. Lobachevskogo, 2012, 202–205
Solvability conditions of de la vall
V. V. Napalkov, “Complex Analysis and the Cauchy Problem for Convolution Operators”, Proc. Steklov Inst. Math., 235 (2001), 158–161
A. B. Sekerin, “On the representation of analytic functions of several variables by exponential series”, Russian Acad. Sci. Izv. Math., 40:3 (1993), 503–527
V. V. Napalkov, A. W. Komarov, “On the expansion of analytic functions in a series of elementary solutions of a convolution equation”, Math. USSR-Sb., 69:2 (1991), 597–605
A. B. Sekerin, “On sufficient sets in spaces of entire functions of several variables”, Math. USSR-Sb., 64:1 (1989), 263–276
Yu. F. Korobeinik, “Inductive and projective topologies. Sufficient sets and representing systems”, Math. USSR-Izv., 28:3 (1987), 529–554
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