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Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 2, Pages 309–341 (Mi izv1685)  

This article is cited in 20 scientific papers (total in 21 papers)

Local description of closed ideals and submodules of analytic functions of one variable. II

I. F. Krasichkov-Ternovskii


Abstract: Let $P$ be a topological module (over the ring of polynomials) of vector-valued functions $f\colon G\to\mathbf C^q$ holomorphic in a domain $G\subset\mathbf C$. In the first part of this article it was established that to solve the local description problem for closed submodules of $P$ it suffices to verify two properties – stability and saturation. In the present second part various methods of carrying out this verification are elaborated. Conditions are presented under which closed submodules are stable and saturated and, consequently, local. In particular a wide class of locally convex algebras of analytic functions which admit local description of their closed ideals is isolated.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1980, 14:2, 289–316

Bibliographic databases:

UDC: 517.5
MSC: 46J15, 46J20, 46H25
Received: 20.12.1976

Citation: I. F. Krasichkov-Ternovskii, “Local description of closed ideals and submodules of analytic functions of one variable. II”, Izv. Akad. Nauk SSSR Ser. Mat., 43:2 (1979), 309–341; Math. USSR-Izv., 14:2 (1980), 289–316

Citation in format AMSBIB
\Bibitem{Kra79}
\by I.~F.~Krasichkov-Ternovskii
\paper Local description of closed ideals and submodules of analytic functions of one variable.~II
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 2
\pages 309--341
\mathnet{http://mi.mathnet.ru/izv1685}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=534596}
\zmath{https://zbmath.org/?q=an:0432.46049|0408.46035}
\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 14
\issue 2
\pages 289--316
\crossref{https://doi.org/10.1070/IM1980v014n02ABEH001107}


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    This publication is cited in the following articles:
    1. I. F. Krasichkov-Ternovskii, “Spectral synthesis of analytic functions on systems of convex domains”, Math. USSR-Sb., 39:1 (1981), 1–35  mathnet  crossref  mathscinet  zmath  isi
    2. I. F. Krasichkov-Ternovskii, “Spectral synthesis on systems of unbounded convex domains”, Math. USSR-Sb., 39:3 (1981), 343–357  mathnet  crossref  mathscinet  zmath  isi
    3. I. F. Krasichkov-Ternovskii, “Spectral synthesis on systems of convex domains. Extension of the synthesis”, Math. USSR-Sb., 40:1 (1981), 87–105  mathnet  crossref  mathscinet  zmath  isi
    4. I. F. Krasichkov-Ternovskii, “Abstract methods for a local description of closed submodules of analytic functions”, Math. USSR-Sb., 71:2 (1992), 481–497  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. A. B. Shishkin, “Spectral synthesis for an operator generated by multiplication by a power of the independent variable”, Math. USSR-Sb., 73:1 (1992), 211–229  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. I. F. Krasichkov-Ternovskii, “Spectral synthesis in a complex domain for a differential operator with constant coefficients. III: Ample submodules”, Russian Acad. Sci. Sb. Math., 76:1 (1993), 165–188  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. I. F. Krasichkov-Ternovskii, “Spectral synthesis in a complex domain for a differential operator with constant coefficients. II. The module method”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 1–15  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. I. F. Krasichkov-Ternovskii, “The fundamental principle for invariant subspaces of analytic functions. I”, Sb. Math., 188:2 (1997), 195–226  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. A. B. Shishkin, “Spectral synthesis for systems of differential operators with constant coefficients”, Sb. Math., 194:12 (2003), 1865–1898  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. B. N. Khabibullin, “Closed Submodules of Holomorphic Functions with Two Generators”, Funct. Anal. Appl., 38:1 (2004), 52–64  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. B. N. Khabibullin, “Closed Ideals of Holomorphic Functions with Two Generators”, Math. Notes, 76:4 (2004), 558–563  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. 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
    13. “Igor Fedorovich Krasichkov-Ternovskii (13.02.1935–08.03.2012)”, Ufimsk. matem. zhurn., 4:3 (2012), 187–192  mathnet
    14. A. B. Shishkin, “Proektivnoe i in'ektivnoe opisaniya v kompleksnoi oblasti. Dvoistvennost”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:1 (2014), 47–65  mathnet  crossref  elib
    15. N. F. Abuzyarova, “Closed submodules in the module of entire functions of exponential type and polynomial growth on the real axis”, Ufa Math. J., 6:4 (2014), 3–17  mathnet  crossref
    16. T. A. Volkovaya, A. B. Shishkin, “Lokalnoe opisanie tselykh funktsii. Podmoduli ranga 1”, Vladikavk. matem. zhurn., 16:2 (2014), 14–28  mathnet
    17. N. F. Abuzyarova, “Some properties of principal submodules in the module of entire functions of exponential type and polynomial growth on the real axis”, Ufa Math. J., 8:1 (2016), 1–12  mathnet  crossref  isi  elib
    18. N. F. Abuzyarova, “On $2$-generateness of weakly localizable submodules in the module of entire functions of exponential type and polynomial growth on the real axis”, Ufa Math. J., 8:3 (2016), 8–21  mathnet  crossref  mathscinet  isi  elib
    19. N. F. Abuzyarova, “Spectral Synthesis for the Differentiation Operator in the Schwartz Space”, Math. Notes, 102:2 (2017), 137–148  mathnet  crossref  crossref  mathscinet  isi  elib
    20. N. F. Abuzyarova, “Glavnye podmoduli v module Shvartsa”, Izv. vuzov. Matem., 2020, no. 5, 83–88  mathnet  crossref
    21. N. F. Abuzyarova, “Synthesizable sequence and principle submodules in Schwartz module”, Ufa Math. J., 12:3 (2020), 11–21  mathnet  crossref  isi
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