6 papers
On the Distribution of Zero Sets of Holomorphic Functions. IV. A Criterion
B. N. Khabibullin, E. B. Men'shikova
Let be a proper domain in the extended complex plane , be a difference of non-trivial subharm…
Order version of the Hahn-Banach theorem, and envelopes. II. Applications to the function theory
B. N. Khabibullin, A. P. Rozit, E. B. Khabibullina
Chapter 1 deals with the problem of the existence of an upper/lower envelope from a convex cone or, more generally, a convex set for functions on the projective limit of vector lat…
On the Distribution of Zero Sets of Holomorphic Functions. III. Conversion Theorems
B. N. Khabibullin, F. B. Khabibullin
Let be a domain in the complex plane . It follows from first part of our work that if a non-zero holomorphic function on vanishes on a sequence ${\sf Z}\subs…
On the Distribution of Zero Sets of Holomorphic Functions. II
B. N. Khabibullin, E. B. Khabibullina
Let be a nonempty domain in . We give a scale of necessary conditions for the distribution of the zero set of holomorphic function on domain $D\subset {\mathbb…
On the Distribution of Zero Sets of Holomorphic Functions
B. N. Khabibullin, A. P. Rozit
Let be a subharmonic function with Riesz measure in a domain in the -dimensional complex Euclidean space , and let be a nonzero function that is h…
The order versions of the Hahn--Banach Theorem and envelopes. I. Homogeneous functions
Bulat Khabibullin, Alexei Rozit, Farkhat Khabibullin
We present here the General formulation of the problem of existence and construction of upper and lower envelope for an arbitrary function with values from the completion of the or…