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

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

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
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. B. N. Khabibullin, “Zero sets for classes of entire functions and a representation of meromorphic functions”, Math. Notes, 59:4 (1996), 440–444
3. Brian J. Cole, Thomas J. Ransford, “Jensen measures and harmonic measures”, crll, 2001:541 (2001), 29
4. B. N. Khabibullin, “On the Growth of Entire Functions of Exponential Type near a Straight Line”, Math. Notes, 70:4 (2001), 560–573
5. B. N. Khabibullin, “On the Rubel–Taylor Problem on a Representation of Holomorphic Functions”, Funct. Anal. Appl., 35:3 (2001), 237–239
6. B. N. Khabibullin, “Dual representation of superlinear functionals and its applications in function theory. I”, Izv. Math., 65:4 (2001), 835–852
7. B. N. Khabibullin, “Growth of Entire Functions with Given Zeros and Representation of Meromorphic Functions”, Math. Notes, 73:1 (2003), 110–124
8. L. Yu. Cherednikova, “Nonuniqueness Sequences for Weighted Algebras of Holomorphic Functions in the Unit Circle”, Math. Notes, 77:5 (2005), 715–725
9. B. N. Khabibullin, “Zero subsets, representation of meromorphic functions, and Nevanlinna characteristics in a disc”, Sb. Math., 197:2 (2006), 259–279
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
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
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