Vestnik КRAUNC. Fiz.-Mat. Nauki. 2023. vol. 42. no. 1. P. 150-163. ISSN 2079-6641

Research Article
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MSC 35K05, 35K15

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

R. Shamoyan^{*,1}, O. Mihi´c^{*,2}

¹Bryansk State University, Russia, 241050, Bryansk
²University of Belgrade, Faculty of Organizational Sciences, Serbia, Belgrade, Jove Ili´ca 154.

Abstract. 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.

Key words: Blaschke type infinite products, area Nevanlinna – type spaces, Nevanlinna characteristic, parametric representations, analytic function.

Received: 15.08.2022; Revised: 25.12.2022; Accepted: 24.03.2023; First online: 16.04.2023

For citation. Shamoyan R., Mihi´c O. On some new results in large area Nevanlinna spaces in the unit disk. Vestnik KRAUNC. Fiz.-mat. nauki. 2023, 42: 1, 150-163. EDN: DSMGZK.

Funding. Not applicable.

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

^*Correspondence: E-mail:,

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Shamoyan R., Mihi´c O., 2023

© Institute of Cosmophysical Research and Radio Wave Propagation, 2023 (original layout, design, compilation)


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Information about authors

Shamoyan Romi Fayzovich – Ph.D. (Phys. & Math.), Senior Researcher, Department of Mathematical Analysis, Bryansk State University named after Academician I. G. Perovsky, Bryansk, Russia,

Mihic Olivera – Ph.D. (Phys. & Math.), Associate professor, Department of Mathematics, University of Belgrade, Belgrade, Republic of Serbia,