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Izvestiya: Mathematics, 2001, Volume 65, Issue 5, Pages 1017–1039
DOI: https://doi.org/10.1070/IM2001v065n05ABEH000361
(Mi im361)
 

This article is cited in 22 scientific papers (total in 22 papers)

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

B. N. Khabibullin

Bashkir State University
References:
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 Cn, 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.
Received: 25.06.1997
Bibliographic databases:
Language: English
Original paper language: Russian
Citation: B. N. Khabibullin, “Dual representation of superlinear functionals and its applications in function theory. II”, Izv. Math., 65:5 (2001), 1017–1039
Citation in format AMSBIB
\Bibitem{Kha01}
\by B.~N.~Khabibullin
\paper Dual representation of superlinear functionals and its applications in function theory.~II
\jour Izv. Math.
\yr 2001
\vol 65
\issue 5
\pages 1017--1039
\mathnet{http://mi.mathnet.ru/eng/im361}
\crossref{https://doi.org/10.1070/IM2001v065n05ABEH000361}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1874358}
\zmath{https://zbmath.org/?q=an:1052.32004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33747030301}
Linking options:
  • https://www.mathnet.ru/eng/im361
  • https://doi.org/10.1070/IM2001v065n05ABEH000361
  • https://www.mathnet.ru/eng/im/v65/i5/p167
    Cycle of papers
    This publication is cited in the following 22 articles:
    1. E. G. Kudasheva, E. B. Menshikova, B. N. Khabibullin, “Dual construction and existence of (pluri)subharmonic minorant”, Ufa Math. J., 16:3 (2024), 65–73  mathnet  crossref
    2. B. N. Khabibullin, “Subharmonic envelopes for functions on domains”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 29:3 (2023), 64–71  mathnet  mathnet  crossref
    3. B. N. Khabibullin, E. B. Menshikova, “Preorders on Subharmonic Functions and Measures with Applications to the Distribution of Zeros of Holomorphic Functions”, Lobachevskii J Math, 43:3 (2022), 587  crossref
    4. B. N. Khabibullin, “Poisson–Jensen formulas and balayage of measures”, Eurasian Math. J., 12:4 (2021), 53–73  mathnet  crossref
    5. Khabibullin B.N., “Balayage of Measures With Respect to (Sub-)Harmonic Functions”, Lobachevskii J. Math., 41:11, SI (2020), 2179–2189  crossref  mathscinet  isi
    6. 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  mathscinet  elib
    7. B. N. Khabibullin, A. V. Shmelyova, “Balayage of measures and subharmonic functions on a system of rays. I. Classic case”, St. Petersburg Math. J., 31:1 (2020), 117–156  mathnet  crossref  isi  elib
    8. B. N. Khabibullin, A. P. Rozit, E. B. Khabibullina, “Order versions of the Hahn–Banach theorem and envelopes. II. Applications to the function theory”, J. Math. Sci. (N. Y.), 257:3 (2021), 366–409  mathnet  crossref  mathscinet
    9. B. N. Khabibullin, E. B. Menshikova, “On the Distribution of Zero Sets of Holomorphic Functions: II”, Funct Anal Its Appl, 53:1 (2019), 65  crossref
    10. 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  mathscinet  isi  elib
    11. B. N. Khabibullin, Z. F. Abdullina, A. P. Rozit, “A uniqueness theorem and subharmonic test functions”, St. Petersburg Math. J., 30:2 (2019), 379–390  mathnet  crossref  mathscinet  isi  elib
    12. 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
    13. 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
    14. 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
    15. 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
    16. B. N. Khabibullin, “Sequences of non-uniqueness for weight spaces of holomorphic functions”, Russian Math. (Iz. VUZ), 59:4 (2015), 63–70  mathnet  crossref
    17. 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
    18. 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
    19. 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
    20. 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
    Citing articles in Google Scholar: Russian citations, English citations
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    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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