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Mat. Sb., 2011, Volume 202, Number 12, Pages 3–22 (Mi msb7864)  

This article is cited in 11 scientific papers (total in 11 papers)

Boundary regularity of Nevanlinna domains and univalent functions in model subspaces

A. D. Baranova, K. Yu. Fedorovskiyb

a St. Petersburg State University, Department of Mathematics and Mechanics
b N. E. Bauman Moscow State Technical University

Abstract: In the paper we study boundary regularity of Nevanlinna domains, which have appeared in problems of uniform approximation by polyanalytic polynomials. A new method for constructing Nevanlinna domains with essentially irregular nonanalytic boundaries is suggested; this method is based on finding appropriate univalent functions in model subspaces, that is, in subspaces of the form $K_\varTheta=H^2\ominus\varTheta H^2$, where $\varTheta$ is an inner function. To describe the irregularity of the boundaries of the domains obtained, recent results by Dolzhenko about boundary regularity of conformal mappings are used.
Bibliography: 18 titles.

Keywords: Nevanlinna domain, model subspace $K_\varTheta$, conformal mapping, inner function, Blaschke product.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm7864

Full text: PDF file (574 kB)
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English version:
Sbornik: Mathematics, 2011, 202:12, 1723–1740

Bibliographic databases:

UDC: 517.542+517.547.5
MSC: Primary 30E10; Secondary 30C20, 30D60
Received: 22.03.2011 and 11.07.2011

Citation: A. D. Baranov, K. Yu. Fedorovskiy, “Boundary regularity of Nevanlinna domains and univalent functions in model subspaces”, Mat. Sb., 202:12 (2011), 3–22; Sb. Math., 202:12 (2011), 1723–1740

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Ya. Mazalov, P. V. Paramonov, K. Yu. Fedorovskiy, “Conditions for $C^m$-approximability of functions by solutions of elliptic equations”, Russian Math. Surveys, 67:6 (2012), 1023–1068  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Proc. Steklov Inst. Math., 279 (2012), 215–229  mathnet  crossref  mathscinet  isi  elib
    3. Fedorovskiy K.Yu., “Uniform and $C^m$-approximation by polyanalytic polynomials”, Complex Analysis and Potential Theory, CRM Proceedings & Lecture Notes, 55, eds. Boivin A., Mashreghi J., Amer. Math. Soc., 2012, 323–329  crossref  mathscinet  zmath  isi
    4. M. Ya. Mazalov, “An example of a non-rectifiable Nevanlinna contour”, St. Petersburg Math. J., 27:4 (2016), 625–630  mathnet  crossref  mathscinet  isi  elib
    5. A. D. Baranov, J. J. Carmona, K. Yu. Fedorovskiy, “Density of certain polynomial modules”, J. Approx. Theory, 206 (2016), 1–16  crossref  mathscinet  zmath  scopus
    6. K. Yu. Fedorovskiy, “On the density of certain modules of polyanalytic type in spaces of integrable functions on the boundaries of simply connected domains”, Sb. Math., 207:1 (2016), 140–154  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. E. V. Borovik, K. Yu. Fedorovskiy, “On the Relationship Between Nevanlinna and Quadrature Domains”, Math. Notes, 99:3 (2016), 460–464  mathnet  crossref  crossref  mathscinet  isi  elib
    8. M. Ya. Mazalov, “On Nevanlinna domains with fractal boundaries”, St. Petersburg Math. J., 29:5 (2018), 777–791  mathnet  crossref  mathscinet  isi  elib
    9. Baranov A.D., Fedorovskiy K.Yu., “on l (1)-Estimates of Derivatives of Univalent Rational Functions”, J. Anal. Math., 132 (2017), 63–80  crossref  mathscinet  zmath  isi  scopus
    10. Yu. S. Belov, K. Yu. Fedorovskiy, “Model spaces containing univalent functions”, Russian Math. Surveys, 73:1 (2018), 172–174  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    11. Belov Yu., Borichev A., Fedorovskiy K., “Nevanlinna Domains With Large Boundaries”, J. Funct. Anal., 277:8 (2019), 2617–2643  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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