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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 3, Pages 539–565 (Mi izv1500)  

This article is cited in 18 scientific papers (total in 18 papers)

Inductive and projective topologies. Sufficient sets and representing systems

Yu. F. Korobeinik


Abstract: Conditions are found for the equality of various topologies in inductive limits of spaces of functions defined on an arbitrary set. A new class of sufficient sets is introduced and its connection with classes studied previously is determined. The general dependence between weakly sufficient sets and absolutely representing systems is indicated.
Bibliography: 32 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 28:3, 529–554

Bibliographic databases:

UDC: 517.9
MSC: Primary 30D10, 30E20, 46A12; Secondary 30B50, 30D15, 46A14
Received: 11.04.1985

Citation: Yu. F. Korobeinik, “Inductive and projective topologies. Sufficient sets and representing systems”, Izv. Akad. Nauk SSSR Ser. Mat., 50:3 (1986), 539–565; Math. USSR-Izv., 28:3 (1987), 529–554

Citation in format AMSBIB
\Bibitem{Kor86}
\by Yu.~F.~Korobeinik
\paper Inductive and projective topologies. Sufficient sets and representing systems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 3
\pages 539--565
\mathnet{http://mi.mathnet.ru/izv1500}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=854595}
\zmath{https://zbmath.org/?q=an:0628.46004}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 28
\issue 3
\pages 529--554
\crossref{https://doi.org/10.1070/IM1987v028n03ABEH000896}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. Yu. F. Korobeinik, “Representative systems of exponentials and the Cauchy problem for partial differential equations with constant coefficients”, Izv. Math., 61:3 (1997), 553–592  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. J. Bonet, S.N. Melikhov, “Interpolation of Entire Functions and Projective Descriptions”, Journal of Mathematical Analysis and Applications, 205:2 (1997), 454  crossref
    4. Korobeinik Y.F., “On absolutely representing systems in spaces of infinitely differentiable functions”, Studia Mathematica, 139:2 (2000), 175–188  isi  elib
    5. José Bonet, PawełDomański, “Sampling sets and sufficient sets for A−∞”, Journal of Mathematical Analysis and Applications, 277:2 (2003), 651  crossref
    6. A. V. Abanin, “Ob odnom primenenii slabo dostatochnykh mnozhestv”, Vladikavk. matem. zhurn., 7:2 (2005), 11–16  mathnet  mathscinet  elib
    7. A. V. Abanin, “O probleme Brannana dlya dostatochnykh mnozhestv”, Vladikavk. matem. zhurn., 7:3 (2005), 5–10  mathnet  mathscinet  elib
    8. B. N. Khabibullin, “Dva obschikh usloviya nedopustimosti spektralnogo sinteza dlya invariantnykh podprostranstv golomorfnykh funktsii”, Vladikavk. matem. zhurn., 7:3 (2005), 71–78  mathnet  mathscinet  elib
    9. S. N. Melikhov, Z. Momm, “O svoistve vnutr-prodolzhaemosti predstavlyayuschikh sistem eksponent na vypuklykh lokalno zamknutykh mnozhestvakh”, Vladikavk. matem. zhurn., 10:2 (2008), 36–45  mathnet  mathscinet  elib
    10. Yu. F. Korobeinik, “The absolutely representing families in certain classes of locally convex spaces”, Russian Math. (Iz. VUZ), 53:9 (2009), 20–28  mathnet  crossref  mathscinet  zmath  elib
    11. Alexander V. Abanin, Le Hai Khoi, “On the duality between and for convex domains”, Comptes Rendus Mathematique, 347:15-16 (2009), 863  crossref
    12. A. V. Abanin, Le Hai Khoi, “Pre-dual of the Function Algebra A −∞(D) and Representation of Functions in Dirichlet Series”, Complex anal oper theory, 2010  crossref
    13. D. A. Abanina, “Representation of solutions of convolution equations in nonquasianalytic Beurling classes of ultradifferentiable functions of mean type”, Russian Math. (Iz. VUZ), 55:6 (2011), 1–8  mathnet  crossref  mathscinet  elib
    14. A.V. Abanin, L.H. Khoi, “Mutual dualities betweenA−∞(Ω) and for lineally convex domains”, Complex Variables and Elliptic Equations, 2012, 1  crossref
    15. 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
    16. D. A. Polyakova, “On solutions of convolution equations in spaces of ultradifferentiable functions”, St. Petersburg Math. J., 26:6 (2015), 949–963  mathnet  crossref  mathscinet  isi  elib  elib
    17. A. V. Abanin, “Sampling sets for the space of holomorphic functions of polynomial growth in a ball”, Ufa Math. J., 7:4 (2015), 3–14  mathnet  crossref  elib
    18. D. A. Polyakova, “O chastnom reshenii neodnorodnogo uravneniya svertki v prostranstvakh ultradifferentsiruemykh funktsii”, Vladikavk. matem. zhurn., 20:4 (2018), 67–75  mathnet  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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