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Izv. RAN. Ser. Mat., 1993, Volume 57, Issue 1, Pages 129–146 (Mi izv890)  

This article is cited in 11 scientific papers (total in 11 papers)

The theorem on the least majorant and its applications.I. Entire and meromorphic functions

B. N. Khabibullin

Abstract: The general concept of sweeping out is used to generalize the theorem of Koosis on the least superharmonic majorant in $\mathbb C$ to least majorants with respect to a convex cone of functions defined in a domain in $\mathbb R^k$ or $\mathbb C^n$. This generalization is applied to the description of nontrivial ideals and analytic sets of nonuniqueness of codimension 1 in algebras of entire functions, and to the representation of meromorphic functions of given growth.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1994, 42:1, 115–131

Bibliographic databases:

UDC: 517.555
MSC: Primary 32A30, 32A22, 32A20, 30D99, 32E25; Secondary 31B05, 31C10, 32F05, 46E25, 30D50
Received: 24.09.1991

Citation: B. N. Khabibullin, “The theorem on the least majorant and its applications.I. Entire and meromorphic functions”, Izv. RAN. Ser. Mat., 57:1 (1993), 129–146; Russian Acad. Sci. Izv. Math., 42:1 (1994), 115–131

Citation in format AMSBIB
\by B.~N.~Khabibullin
\paper The theorem on the least majorant and its applications.I.~Entire and meromorphic functions
\jour Izv. RAN. Ser. Mat.
\yr 1993
\vol 57
\issue 1
\pages 129--146
\jour Russian Acad. Sci. Izv. Math.
\yr 1994
\vol 42
\issue 1
\pages 115--131

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    This publication is cited in the following articles:
    1. B. N. Khabibullin, “The theorem on the least majorant and its applications. II. Entire and meromorphic functions of finite order”, Russian Acad. Sci. Izv. Math., 42:3 (1994), 479–500  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. B. N. Khabibullin, “Zero sets for classes of entire functions and a representation of meromorphic functions”, Math. Notes, 59:4 (1996), 440–444  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Brian J. Cole, Thomas J. Ransford, “Jensen measures and harmonic measures”, crll, 2001:541 (2001), 29  crossref  mathscinet
    4. B. N. Khabibullin, “On the Growth of Entire Functions of Exponential Type near a Straight Line”, Math. Notes, 70:4 (2001), 560–573  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. B. N. Khabibullin, “On the Rubel–Taylor Problem on a Representation of Holomorphic Functions”, Funct. Anal. Appl., 35:3 (2001), 237–239  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. B. N. Khabibullin, “Dual representation of superlinear functionals and its applications in function theory. I”, Izv. Math., 65:4 (2001), 835–852  mathnet  crossref  crossref  mathscinet  zmath
    7. B. N. Khabibullin, “Growth of Entire Functions with Given Zeros and Representation of Meromorphic Functions”, Math. Notes, 73:1 (2003), 110–124  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. 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
    9. 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
    10. 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
    11. B. N. Khabibullin, A. P. Rozit, E. B. Khabibullina, “Poryadkovye versii teoremy Khana—Banakha i ogibayuschie. II. Primeneniya v teorii funktsii”, Kompleksnyi analiz. Matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 162, VINITI RAN, M., 2019, 93–135  mathnet  mathscinet
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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