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Bulat N. Khabibullin

Publications and source records attributed to Bulat N. Khabibullin.

24 records · Page 2Linked to original sources
arXiv2011

Distribution of zero subsequences for Bernstein space and criteria of completeness for exponential system on a segment

For $σ\in (0,+\infty)$, denote by $B_σ^{\infty}$ the Bernstein space (of type $σ$) of all entire functions of exponential type $\leq σ$ bounded on real axis $\R$. Let $I_d\subset \R$ be a segment of length $d>0$. We announce complete description of non-uniqueness sequences of points for $B_σ^\infty$ and criteria of completeness of exponential system in $C(I_d)$ or $L^p(I_d)$ to within one or two exponential functions.

math.CV↗
arXiv2011

Nevanlinna's Theorems

We give a short survey on generalizations of Nevanlinna's theorems on zero distribution of bounded holomorphic functions and representation of meromorphic functions in multiply connected domains. It is a part of our report in the conference on complex analysis dedicated to the memory of Anatolii Asirovich Goldberg in Lviv, May 31-June 5, 2010.

math.CV↗
arXiv2010

A conjecture on some estimates for integrals

A conjecture concerning some pairs of interfering estimates for some integrals is formulated in three equivalent versions. Its importance for the the Paley problem for plurisubharmonic functions and for certain classes of extremal problems for entire functions of several variables is declared.

math.CV↗
arXiv2005

The representation of a meromorphic function as the quotient of entire functions and Paley problem in C^n: survey of some results

The classical representation problem for a meromorphic function f in C^n, n>=1, consists in representing f as the quotient f=g/h of two entire functions g and h, each with logarithm of modulus majorized by a function as close as possible to the Nevanlinna characteristic. Here we introduce generalizations of the Nevanlinna characteristic and give a short survey of classical and recent results on the representation of a meromorphic function in terms such characteristics. When f has a finite lower order, the Paley problem on best possible estimates of the growth of entire functions g and h in the representations f=g/h will be considered. Also we point out to some unsolved problems in this area.

math.CV↗
arXiv2005

Dual Approach to Certain Questions for Weighted Spaces of Holomorphic Functions

We set new dual problems for the weighted spaces of holomorphic functions of one variable in domains on the complex plane, namely: nontriviallity of a given space, description of zero sets, description of (non-)uniqueness sets, the representation of meromorphic functions as a quotient of holomorphic functions from a given space.

math.CV↗