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.
Citation:
B. N. Khabibullin, “Dual representation of superlinear functionals and its applications in function theory. II”, Izv. Math., 65:5 (2001), 1017–1039
This publication is cited in the following 22 articles:
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
B. N. Khabibullin, “Subharmonic envelopes for functions on domains”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 29:3 (2023), 64–71
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
B. N. Khabibullin, “Poisson–Jensen formulas and balayage of measures”, Eurasian Math. J., 12:4 (2021), 53–73
Khabibullin B.N., “Balayage of Measures With Respect to (Sub-)Harmonic Functions”, Lobachevskii J. Math., 41:11, SI (2020), 2179–2189
E. B. Menshikova, B. N. Khabibullin, “K raspredeleniyu nulevykh mnozhestv golomorfnykh funktsii. II”, Funkts. analiz i ego pril., 53:1 (2019), 84–87
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
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
B. N. Khabibullin, E. B. Menshikova, “On the Distribution of Zero Sets of Holomorphic Functions: II”, Funct Anal Its Appl, 53:1 (2019), 65
B. N. Khabibullin, A. P. Rozit, “On the Distribution of Zero Sets of Holomorphic Functions”, Funct. Anal. Appl., 52:1 (2018), 21–34
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
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
T. Yu. Baiguskarov, B. N. Khabibullin, “Holomorphic Minorants of Plurisubharmonic Functions”, Funct. Anal. Appl., 50:1 (2016), 62–65
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
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
B. N. Khabibullin, “Sequences of non-uniqueness for weight spaces of holomorphic functions”, Russian Math. (Iz. VUZ), 59:4 (2015), 63–70
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
B. N. Khabibullin, “Zero sequences of holomorphic functions, representation of meromorphic functions. II. Entire functions”, Sb. Math., 200:2 (2009), 283–312
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
B. N. Khabibullin, “Zero sequences of holomorphic functions, representation
of meromorphic functions, and harmonic minorants”, Sb. Math., 198:2 (2007), 261–298
Citation in format AMSBIB
Contact us: