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Closed Ideals of Holomorphic Functions with Two Generators

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Abstract

For a wide class of algebras P of holomorphic functions on a domain in ℂ, sufficient conditions are obtained under which a closed ideal I ⊂ P is 2-generated.

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REFERENCES

  1. I.F. Krasichkov-Ternovskii,"Local description o closed ideals and submodules of analytic functions of a single variable.I,"Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],43 (1979),no.1,44–66.

  2. I.F. Krasichkov-Ternovskii,"Local description o closed ideals and submodules of analytic functions of a single variable.II,"Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],43 (1979),no.2,309–341.

  3. N.K. Nikol skii,"Elementary description o the methods o localizing ideals,"Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI),170 (1989),207–232.

    Google Scholar 

  4. F.A. Shamoyan,"Division theorems and closed ideals in algebras of analytic functions with a majorant of nite growth,"Izv. Akad. Nauk Armyan. SSR Ser. Mat.,15 (1980),no.4,323–331.

  5. J.J. Kelleher and B.A. Taylor,"Closed ideals in locally convex algebras of analytic functions,"J. Reine Angew. Math.,255 (1972),190–209.

    Google Scholar 

  6. R.W. Braun,"Weighted algebras of entire functions in which each closed ideal admits two algebraic generators,"Mich. Math. J.,34 (1987),no.3,441–450.

    Google Scholar 

  7. B.N. Khabibullin,"Closed ideals and submodules of holomorphic unctions with two generators," in:Geometric Theory of Functions, Boundary Value Problems and Their Applications [in Russian ], Tr.Mat.Tsentra im.N.I.Lobachevskogo,vol.13,Kazan.Mat.Obshch.,Kazan,2002,pp.158–163.

    Google Scholar 

  8. W.A. Squires,"Necessary conditions for universal interpolation in_ E,"Canad. J. Math.,33 (1981), no.6,1356–1364.

    Google Scholar 

  9. B.N. Khabibullin,"Closed submodules of holomorphic unctions generated by submodules that admit a local description,"in:Geometric Theory of Functions, Boundary-Value Problems and Their Appli-cations [in Russian ],Tr.Mat.Tsentraim.N.I.Lobachevskogo,vol.14,Kazan.Mat.Obshch.,Kazan, 2002,pp.280–298.

    Google Scholar 

  10. J.J. Metzger,"Principal local ideals in weighted spaces o entire unctions,"Trans. Amer. Math. Soc., 165 (1972),149–158.

    Google Scholar 

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Authors and Affiliations

  1. Bashkir State University, Institute of Mathematics and Computer Center, Ural Division of the Russian Academy of Sciences, Ufa

    V. N. Khabibullin

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  1. V. N. Khabibullin
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Khabibullin, V.N. Closed Ideals of Holomorphic Functions with Two Generators. Mathematical Notes 76, 558–563 (2004). https://doi.org/10.1023/B:MATN.0000043485.64883.c4

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  • DOI: https://doi.org/10.1023/B:MATN.0000043485.64883.c4

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