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St. Petersburg Mathematical Journal

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Example of a nonrectifiable Nevanlinna contour


Author: M. Ya. Mazalov
Translated by: S. Kislyakov
Original publication: Algebra i Analiz, tom 27 (2015), nomer 4.
Journal: St. Petersburg Math. J. 27 (2016), 625-630
MSC (2010): Primary 30C20
DOI: https://doi.org/10.1090/spmj/1409
Published electronically: June 2, 2016
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Abstract: Nevanlinna contours (and domains) were introduced by K. Yu. Fedorovskiĭ in connection with the problem of uniform approximation of continuous functions by polyanalytic polynomials; also, these contours are related to pseudocontinuation of analytic functions, to the theory of model spaces, etc. An example of a nonrectifiable Nevanlinna contour is constructed in this paper for the first time.


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Additional Information

M. Ya. Mazalov
Affiliation: National Research University “Moscow energy institute”, Energeticheskiĭ proezd 1, Smolensk, Russia
Email: maksimmazalov@yandex.ru

DOI: https://doi.org/10.1090/spmj/1409
Keywords: Nevanlinna contours and domains, conformal mapping, univalent functions, Blaschke condition, polyanalytic functions
Received by editor(s): February 10, 2015
Published electronically: June 2, 2016
Additional Notes: The author was supported in part by RFBR (grant no. 12-01-00434-a), and by the program “Leading Scientific Schools of the Russian Federation” (grant no. NSh-2900.2014.1)
Article copyright: © Copyright 2016 American Mathematical Society

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