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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



On Nevanlinna domains with fractal boundaries

Author: M. Ya. Mazalov
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 29 (2017), nomer 5.
Journal: St. Petersburg Math. J. 29 (2018), 777-791
MSC (2010): Primary 30C20
Published electronically: July 26, 2018
MathSciNet review: 3724640
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Abstract | References | Similar Articles | Additional Information

Abstract: A positive answer is given to the question on the existence of a Nevanlinna contour of Hausdorff dimension exceeding $1$, posed by K. Yu. Fedorovskiĭ in 2001. In particular, it is shown that this dimension may exceed $3/2$.

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Additional Information

M. Ya. Mazalov
Affiliation: Smolensk branch, National Research University “Moscow Energy Institute”, Smolensk, Russia — and — Moscow N. E. Bauman State Technical university, Moscow, Russia

Keywords: Nevanlinna contours and domains, conformal mapping, univalent functions, Blaschke condition, polyanalytic functions, fractals
Received by editor(s): May 30, 2017
Published electronically: July 26, 2018
Additional Notes: Supported by Ministry of Education and Science of RF (project no. 1.3843.2017), by RFBR (project no. 16-01-00674), and by the Programme for support of the Leading Scientific Schools in RF (project no. SS-9110.2016.1).
Article copyright: © Copyright 2018 American Mathematical Society