On Some New Results in Large Area Nevanlinna Spaces in the Unit Disk

2023

Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, Vol 2023, Iss 1, Pp 150-163 (2023)

The study of various infinite products in various spaces of analytic functions in the unit disk is a well known and well studied problem of complex function theory in the unit disk. The goal of our paper is to study so-called Blashcke type products in new large, general analytic area Nevanlinna spaces in the unit disk.A new approach is suggested in this paper, namely we prove, use and apply various new embedding theorems which relate new general, large analytic area Nevanlinna spaces with less general well-studied and wellknown such type analytic spaces in the unit disk. Our theorems can be applied or can be used even in more general situation, when we consider large, general analytic area Nevanlinna spaces not in the unit disk, but in the circular ring.In our paper, using same approach new parametric representations of mentioned large, general analytic area Nevanlinna spaces are presented. These results also can be applied or used in the future to obtain more general theorems on parametric representations of mentioned large,general area Nevanlinna type spaces not in the unit disk, but in more general circular domains.

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KamGU by Vitus Bering, 2023.

blaschke type infinite products, area nevanlinna – type spaces, nevanlinna characteristic, parametric representations, analytic function, бесконечные произведения типа бляшке, площадь пространств неванлинновского типа, характеристика неванлинны, параметрические представления, аналитическая функция, Science