A. Rozit

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math.CV2018

On the Distribution of Zero Sets of Holomorphic Functions. IV. A Criterion

B. N. Khabibullin, E. B. Men'shikova

Let $D$ be a proper domain in the extended complex plane $C_{\infty} := C \cup {\infty}$ , $M = M_{+} - M_{-} \neq \equiv \pm \infty$ be a difference of non-trivial subharm…

math.CV2018

On the Distribution of Zero Sets of Holomorphic Functions. III. Conversion Theorems

B. N. Khabibullin, F. B. Khabibullin

Let $D$ be a domain in the complex plane $C$ . It follows from first part of our work that if a non-zero holomorphic function $f$ on $D$ vanishes on a sequence ${\sf Z}\subs…

math.CV2018

On the Distribution of Zero Sets of Holomorphic Functions. II

B. N. Khabibullin, E. B. Khabibullina

Let $D$ be a nonempty domain in $C^{n}$ . We give a scale of necessary conditions for the distribution of the zero set of holomorphic function $f$ on domain $D\subset {\mathbb…

math.CV2018

On the Distribution of Zero Sets of Holomorphic Functions

B. N. Khabibullin, A. P. Rozit

Let $M$ be a subharmonic function with Riesz measure $ν_{M}$ in a domain $D$ in the $n$ -dimensional complex Euclidean space $C^{n}$ , and let $f$ be a nonzero function that is h…