Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
24.05.1958
Phone: +7(347) 2 73 67 18
Fax: +7 (347) 2 29 96 65
E-mail: Website: https://matem.anrb.ru/ru/khabibullinbn Keywords: holomorphic function,
entire function,
meromorphic function,
completeness of systems of functions,
minimality of systems of functions,
excesses of systems of functions,
zero set,
set of uniqueness,
potential theory,
subharmonic function,
plurisubharmonic function,
extremal problems of function theory,
vector lattice,
superlinear functional,
projective limit of ordered vector spaces,
balayage,
Jensen measure,
spectral synthesis,
local description of submodules (ideals) in spaces of functions,
convex setю.
UDC: 512.55, 512.562, 514.17, 517.53, 517.538, 517.538.2, 517.54, 517.547, 517.547.2, 517.547.22, 517.55, 517.57, 517.574, 517.581, 517.98, 517.982, 517.16 MSC: 30Dxx, 30Exx, 30H05, 31-xx, 32Axx, 32Kxx, 32Uxx, 46-xx, 06Bxx, 13Cxx, 42A65, 52Axx, 30C15, 30D30, 31A05, 31A15
Subject:
A general scheme of a dual representatin of superlinear functional on projective limits of vector lattices was developed. This scheme give new dual settings for series of problems for weighted spaces of holomorphic functions of one and several variables in domains of the $n$-dimensional complex space, namely: nontriviallity of a given space, description of zero sets, description of (non-)uniqueness sets, existence of holomorphic multipliers from certain classes, "damping" the growth of a given holomorphic function, the representation of meromorphic functions as a quotient of holomorphic functions from a given space. A complete solution of Rubel–Taylor problem on the representation of a meromorphic function of several variables as a quotient of entire functins of least growth is obtained under minimal below boundary of the growth of generalized Nevanlinna characteristic of the meromorphic function. New sufficient conditions for sets of (non-)uniqueness in weight spaces of holomorphic functions in the unit disk and in weight spaces of entire functions are obtained. Paley problem is solved for meromorphic, entire and plurisubharmonic functions. Conditions of completeness of exponential systems in spaces of holomorphic functions on a domain is established in terms of sequences of exponents of these exponential systems and in terms of geometric characteristics of the domain. New conditions of the stability of completeness and minimality of exponential systems are obtained for Banach spaces of functions in a domain or on an Jordan curve (generalization of Redheffer–Alexander theorem for segment). These conditions are formulated in terms of shifts of exponents of exponential systems. The general and at the same time easily checked conditions are established under which each closed ideal (submodule resp.) in algebras (spaces resp.) of holomorphic or differentiable functions of one variable it is generated (topologically) no more than to two generators; for wide classes of spaces of holomorphic functions conditions under which the intersection of invariant concerning differentiation subspaces admitting to spectral synthesis inherits whether or not this property are received.
Main publications:
B. N. Khabibullin, “Closed Submodules of Holomorphic Functions with Two Generators”, Funct. Anal. Appl., 38:1 (2004), 52–64Full Text in English
B. N. Khabibullin, “Excess of systems of exponentials in a domain, and directional convexity deficiency of a curve”, St. Petersburg Math. J., 13:6 (2002), 1047–1080Full Text in English
B. N. Khabibullin, “Dual representation of superlinear functionals and its applications in function theory. II”, Izv. Math., 65:5 (2001), 1017–1039Full Text in English
B. N. Khabibullin, “Paley problem for plurisubharmonic functions of finite lower order”, Sb. Math., 190:2 (1999), 309–321Full Text in English
B. N. Khabibullin, “Sets of uniqueness in spaces of entire functions of a single variable”, Math. USSR-Izv., 39:2 (1992), 1063–1084Full Text in English
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