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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 5, Pages 1088–1099 (Mi izv1599)  

This article is cited in 10 scientific papers (total in 10 papers)

On discrete weakly sufficient sets in certain spaces of entire functions

V. V. Napalkov

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.

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English version:
Mathematics of the USSR-Izvestiya, 1982, 19:2, 349–357

Bibliographic databases:

UDC: 517.5
MSC: Primary 30B50, 30D10, 30D15; Secondary 46A12, 46E10
Received: 29.01.1981

Citation: V. V. Napalkov, “On discrete weakly sufficient sets in certain spaces of entire functions”, Izv. Akad. Nauk SSSR Ser. Mat., 45:5 (1981), 1088–1099; Math. USSR-Izv., 19:2 (1982), 349–357

Citation in format AMSBIB
\by V.~V.~Napalkov
\paper On~discrete weakly sufficient sets in certain spaces of entire functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 5
\pages 1088--1099
\jour Math. USSR-Izv.
\yr 1982
\vol 19
\issue 2
\pages 349--357

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    This publication is cited in the following articles:
    1. Yu. F. Korobeinik, “Inductive and projective topologies. Sufficient sets and representing systems”, Math. USSR-Izv., 28:3 (1987), 529–554  mathnet  crossref  mathscinet  zmath
    2. A. B. Sekerin, “On sufficient sets in spaces of entire functions of several variables”, Math. USSR-Sb., 64:1 (1989), 263–276  mathnet  crossref  mathscinet  zmath
    3. 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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. 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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. V. V. Napalkov, “Complex Analysis and the Cauchy Problem for Convolution Operators”, Proc. Steklov Inst. Math., 235 (2001), 158–161  mathnet  mathscinet  zmath
    6. V. V. Napalkov, A. A. Nuyatov, “The multipoint de la Vallée-Poussin problem for a convolution operator”, Sb. Math., 203:2 (2012), 224–233  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Nuyatov A.A., “Usloviya razreshimosti mnogotochechnoi zadachi valle pussena dlya operatorov svertki”, Vestnik nizhegorodskogo universiteta im. N.I. Lobachevskogo, 2012, 202–205  elib
    8. A. V. Abanin, V. A. Varziev, “Sufficient sets in weighted Fréchet spaces of entire functions”, Siberian Math. J., 54:4 (2013), 575–587  mathnet  crossref  mathscinet  isi
    9. 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  mathnet  crossref  isi  elib
    10. R. A. Bashmakov, K. P. Isaev, R. S. Yulmukhametov, “Predstavlyayuschie sistemy eksponent v vesovykh podprostranstvakh $H(D)$”, Kompleksnyi analiz, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 153, VINITI RAN, M., 2018, 13–28  mathnet  mathscinet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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