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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 4, Pages 205–224 (Mi izv354)  

This article is cited in 2 scientific papers (total in 2 papers)

Dual representation of superlinear functionals and its applications in function theory. I

B. N. Khabibullinab

a Bashkir State University
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: We establish conditions under which there is a dual representation of a superlinear functional on a projective limit of vector lattices. These results will enable us, in the second part of this paper, to pose new dual problems for weighted spaces of holomorphic functions of one or several variables defined on a domain in $\mathbb C^n$, namely, the problems of non-triviality of a given space, description of null sets, description of sets of (non-)uniqueness, existence of holomorphic functions of certain classes that play the role of multipliers “suppressing” the growth of a given holomorphic function, and representation of meromorphic functions by quotients of holomorphic functions from a given space.

DOI: https://doi.org/10.4213/im354

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English version:
Izvestiya: Mathematics, 2001, 65:4, 835–852

Bibliographic databases:

MSC: 47D03, 46A40, 47A20, 47B60, 31B05, 32A30, 30D15, 32U05, 32A15, 31C05
Received: 25.06.1997
Revised: 03.11.2000

Citation: B. N. Khabibullin, “Dual representation of superlinear functionals and its applications in function theory. I”, Izv. RAN. Ser. Mat., 65:4 (2001), 205–224; Izv. Math., 65:4 (2001), 835–852

Citation in format AMSBIB
\Bibitem{Kha01}
\by B.~N.~Khabibullin
\paper Dual representation of superlinear functionals and its applications in function theory.~I
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 4
\pages 205--224
\mathnet{http://mi.mathnet.ru/izv354}
\crossref{https://doi.org/10.4213/im354}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1857717}
\zmath{https://zbmath.org/?q=an:1030.46003}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 4
\pages 835--852
\crossref{https://doi.org/10.1070/IM2001v065n04ABEH000354}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746837793}


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  • https://doi.org/10.4213/im354
  • http://mi.mathnet.ru/eng/izv/v65/i4/p205

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    This publication is cited in the following articles:
    1. B. N. Khabibullin, “Dual representation of superlinear functionals and its applications in function theory. II”, Izv. Math., 65:5 (2001), 1017–1039  mathnet  crossref  crossref  mathscinet  zmath
    2. B. N. Khabibullin, “Zero sequences of holomorphic functions, representation of meromorphic functions, and harmonic minorants”, Sb. Math., 198:2 (2007), 261–298  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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