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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 5, Pages 167–190 (Mi izv361)  

This article is cited in 15 scientific papers (total in 15 papers)

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

B. N. Khabibullin

Bashkir State University

Abstract: The results of the first part of this work (see [1]) are used only in § 7 of this paper, from which subsequent results follow. We pose new dual problems for weight spaces of holomorphic functions of one and several variables defined on a domain in $\mathbb C^n$, namely, the problem of non-triviality of a given space, description of zero sets, description of sets of (non-)uniqueness, existence of holomorphic functions of certain classes that “suppress” the growth of a given holomorphic function, and representation of meromorphic functions as quotients of holomorphic functions contained in a given space.

DOI: https://doi.org/10.4213/im361

Full text: PDF file (1999 kB)
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English version:
Izvestiya: Mathematics, 2001, 65:5, 1017–1039

Bibliographic databases:

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

Citation: B. N. Khabibullin, “Dual representation of superlinear functionals and its applications in function theory. II”, Izv. RAN. Ser. Mat., 65:5 (2001), 167–190; Izv. Math., 65:5 (2001), 1017–1039

Citation in format AMSBIB
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\by B.~N.~Khabibullin
\paper Dual representation of superlinear functionals and its applications in function theory.~II
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 5
\pages 167--190
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\crossref{https://doi.org/10.4213/im361}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1874358}
\zmath{https://zbmath.org/?q=an:1052.32004}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 5
\pages 1017--1039
\crossref{https://doi.org/10.1070/IM2001v065n05ABEH000361}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33747030301}


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    This publication is cited in the following articles:
    1. L. Yu. Cherednikova, “Nonuniqueness Sequences for Weighted Algebras of Holomorphic Functions in the Unit Circle”, Math. Notes, 77:5 (2005), 715–725  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. B. N. Khabibullin, “Zero subsets, representation of meromorphic functions, and Nevanlinna characteristics in a disc”, Sb. Math., 197:2 (2006), 259–279  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. 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
    4. B. N. Khabibullin, F. B. Khabibullin, L. Yu. Cherednikova, “Zero subsequences for classes of holomorphic functions: stability and the entropy of arcwise connectedness. I”, St. Petersburg Math. J., 20:1 (2009), 101–129  mathnet  crossref  mathscinet  zmath  isi
    5. B. N. Khabibullin, “Zero sequences of holomorphic functions, representation of meromorphic functions. II. Entire functions”, Sb. Math., 200:2 (2009), 283–312  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. B. N. Khabibullin, G. R. Talipova, F. B. Khabibullin, “Zero subsequences for Bernstein's spaces and the completeness of exponential systems in spaces of functions on an interval”, St. Petersburg Math. J., 26:2 (2015), 319–340  mathnet  crossref  mathscinet  isi  elib
    7. B. N. Khabibullin, “Sequences of non-uniqueness for weight spaces of holomorphic functions”, Russian Math. (Iz. VUZ), 59:4 (2015), 63–70  mathnet  crossref
    8. T. Yu. Baiguskarov, B. N. Khabibullin, “Holomorphic Minorants of Plurisubharmonic Functions”, Funct. Anal. Appl., 50:1 (2016), 62–65  mathnet  crossref  crossref  mathscinet  isi  elib
    9. B. N. Khabibullin, T. Yu. Baiguskarov, “The Logarithm of the Modulus of a Holomorphic Function as a Minorant for a Subharmonic Function”, Math. Notes, 99:4 (2016), 576–589  mathnet  crossref  crossref  mathscinet  isi  elib
    10. T. Yu. Bayguskarov, G. R. Talipova, B. N. Khabibullin, “Subsequences of zeros for classes of entire functions of exponential type, allocated by restrictions on their growth”, St. Petersburg Math. J., 28:2 (2017), 127–151  mathnet  crossref  mathscinet  isi  elib
    11. R. A. Baladai, B. N. Khabibullin, “From the integral estimates of functions to uniform and locally averaged”, Russian Math. (Iz. VUZ), 61:10 (2017), 11–20  mathnet  crossref  isi
    12. B. N. Khabibullin, A. P. Rozit, “On the Distribution of Zero Sets of Holomorphic Functions”, Funct. Anal. Appl., 52:1 (2018), 21–34  mathnet  crossref  crossref  isi  elib
    13. B. N. Khabibullin, Z. F. Abdullina, A. P. Rozit, “Teorema edinstvennosti i subgarmonicheskie testovye funktsii”, Algebra i analiz, 30:2 (2018), 318–334  mathnet  elib
    14. E. B. Menshikova, B. N. Khabibullin, “K raspredeleniyu nulevykh mnozhestv golomorfnykh funktsii. II”, Funkts. analiz i ego pril., 53:1 (2019), 84–87  mathnet  crossref  elib
    15. B. N. Khabibullin, A. V. Shmelëva, “Vymetanie mer i subgarmonicheskikh funktsii na sistemu luchei. I. Klassicheskii sluchai”, Algebra i analiz, 31:1 (2019), 156–210  mathnet
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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