Loading [MathJax]/jax/output/CommonHTML/jax.js
Mathematics of the USSR-Izvestiya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mathematics of the USSR-Izvestiya, 1981, Volume 17, Issue 2, Pages 299–337
DOI: https://doi.org/10.1070/IM1981v017n02ABEH001355
(Mi im1951)
 

This article is cited in 25 scientific papers (total in 25 papers)

Interpolation problems, nontrivial expansions of zero, and representing systems

Yu. F. Korobeinik
References:
Abstract: Let G be a convex domain with support function h(φ), and let {λk} be distinct complex numbers. In this paper the author determines when the system {eλkz} is absolutely representing in the space A(G) of functions analytic in G, with the topology of uniform convergence on compact sets. In particular he proves the
Theorem. {\it Let L(λ) be an exponential function with indicator h(φ) and simple zeros {λn}n=1. For the system {eλkz}k=1 to be absolutely representing in A(G) it is necessary and sufficient that either of the following two conditions hold}:
1) {\it The system {eλkz}k=1 has a nontrivial expansion of zero in A(G), i.e. n=1bneλnz=0 for every zG}. \smallskip
2) L(λ) is a function of completely regular growth and there exists a function C(λ) of class [1,0] such that
¯limn[1|λn|ln|C(λn)L(λn)|+h(argλn)]0.

Bibliography: 16 titles.
Received: 12.04.1979
Bibliographic databases:
UDC: 517.9
MSC: Primary 30B50, 30D10, 30D15, 30E05; Secondary 30B60, 30C15, 46A06, 46A45
Language: English
Original paper language: Russian
Citation: Yu. F. Korobeinik, “Interpolation problems, nontrivial expansions of zero, and representing systems”, Math. USSR-Izv., 17:2 (1981), 299–337
Citation in format AMSBIB
\Bibitem{Kor80}
\by Yu.~F.~Korobeinik
\paper Interpolation problems, nontrivial expansions of zero, and representing systems
\jour Math. USSR-Izv.
\yr 1981
\vol 17
\issue 2
\pages 299--337
\mathnet{http://mi.mathnet.ru/eng/im1951}
\crossref{https://doi.org/10.1070/IM1981v017n02ABEH001355}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=595258}
\zmath{https://zbmath.org/?q=an:0471.30003|0445.30004}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1981MW12400004}
Linking options:
  • https://www.mathnet.ru/eng/im1951
  • https://doi.org/10.1070/IM1981v017n02ABEH001355
  • https://www.mathnet.ru/eng/im/v44/i5/p1066
  • This publication is cited in the following 25 articles:
    1. S. N. Melikhov, “Coefficients of exponential series for analytic functions and the Pommiez operator”, J. Math. Sci. (N. Y.), 257:2 (2021), 206–245  mathnet  crossref  mathscinet
    2. Kate Overmoyer, Steven M. Seubert, “Non-Synthetic diagonal operators on the space of functions analytic on the unit disk”, Rocky Mountain J. Math., 45:4 (2015)  crossref
    3. Steven M. Seubert, “Common cyclic vectors for diagonal operators on the space of entire functions”, Rocky Mountain J. Math., 44:1 (2014)  crossref
    4. 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
    5. O. A. Krivosheeva, A. S. Krivosheev, “A Criterion for the Fundamental Principle to Hold for Invariant Subspaces on Bounded Convex Domains in the Complex Plane”, Funct. Anal. Appl., 46:4 (2012), 249–261  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. A. V. Abanin, S. V. Petrov, “Minimalnye absolyutno predstavlyayuschie sistemy eksponent v prostranstvakh analiticheskikh funktsii s zadannoi granichnoi gladkostyu”, Vladikavk. matem. zhurn., 14:3 (2012), 13–30  mathnet
    7. Kovalenko M.D., Shulyakovskaya T.D., “Razlozheniya po funktsiyam fadlya-papkovicha v polose. osnovy teorii”, Izvestiya Rossiiskoi akademii nauk. Mekhanika tverdogo tela, 2011, no. 5, 78–98  elib
    8. Abanin A.V., Petrov S.V., “Nekotorye svoistva absolyutno predstavlyayuschikh sistem eksponent i prosteishikh drobei v prostranstvakh analiticheskikh funktsii s zadannoi granichnoi gladkostyu”, Matematicheskii forum (Itogi nauki. Yug Rossii), 5 (2011), 121–126 Some properties of absolutely representing systems of exponential functions and partial fractions in spaces of holomorphic functions with given boundary smoothness  elib
    9. Yu. F. Korobeinik, “Nekotorye voprosy teorii lineinykh topologicheskikh prostranstv (polnota, netrivialnye razlozheniya nulya i porozhdayuschie ikh elementy)”, Vladikavk. matem. zhurn., 12:3 (2010), 47–55  mathnet  elib
    10. O. A. Krivosheeva, A. S. Krivosheev, “Fundamentalnyi printsip dlya invariantnykh podprostranstv”, Ufimsk. matem. zhurn., 2:4 (2010), 58–73  mathnet  zmath  elib
    11. V. B. Sherstyukov, “Nontrivial expansions of zero and representation of analytic functions by series of simple fractions”, Siberian Math. J., 48:2 (2007), 369–381  mathnet  crossref  mathscinet  zmath  isi  elib
    12. S. N. Melichow, “Über absolut repräsentierende Systeme aus Quasipolynomen in Räumen analytischer Funktionen”, Math Nachr, 158:1 (2006), 299  crossref
    13. A. S. Krivosheev, “A fundamental principle for invariant subspaces in convex domains”, Izv. Math., 68:2 (2004), 291–353  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. Yu. F. Korobeinik, “O lineinykh sistemakh uravnenii v operatorakh obobschennoi svertki”, Vladikavk. matem. zhurn., 6:2 (2004), 39–49  mathnet  mathscinet  zmath  elib
    15. S. N. Melikhov, E. V. Teknechyan, “On the expansion of analytic functions in series in successive derivatives”, Russian Math. (Iz. VUZ), 47:2 (2003), 74–78  mathnet  mathscinet  zmath  elib
    16. S. N. Melikhov, “Extension of entire functions of completely regular growth and right inverse to the operator of representation of analytic functions by quasipolynomial series”, Sb. Math., 191:7 (2000), 1049–1073  mathnet  crossref  crossref  mathscinet  zmath  isi
    17. Korobeinik Y.F., “The Fourier method in the Cauchy problem and absolutely representing systems of exponentials. I”, Differential Equations, 35:12 (1999), 1693–1701  mathnet  isi  elib
    18. A. V. Abanin, “Nontrivial expansions of zero and absolutely representing systems”, Math. Notes, 57:4 (1995), 335–344  mathnet  crossref  mathscinet  zmath  isi
    19. Yu. F. Korobeinik, “Nontrivial expansions of zero in absolutely representing systems. Application to convolution operators”, Math. USSR-Sb., 73:1 (1992), 49–66  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    20. Yu. F. Korobeinik, “Description of the general form of nontrivial expansions of zero in exponentials. Applications”, Math. USSR-Izv., 39:2 (1992), 1013–1032  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:524
    Russian version PDF:275
    English version PDF:26
    References:90
    First page:1
     
      Contact us:
    math-net2025_03@mi-ras.ru
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025