K. Yu. Fedorovskiy, “On Some Properties and Examples of Nevanlinna Domains”, Complex analysis and applications, Collected papers, Trudy Mat. Inst. Steklova, 253, Nauka, MAIK «Nauka/Inteperiodika», M., 2006, 204–213; Proc. Steklov Inst. Math., 253 (2006), 186

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Volume 253, Pages 204–213 (Mi tm93)

This article is cited in 23 scientific papers (total in 23 papers)

On Some Properties and Examples of Nevanlinna Domains

K. Yu. Fedorovskiy

Institute of Information Systems in Management at the State University of Management

Full-text PDF (199 kB) Citations (23)

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Abstract: The properties of Nevanlinna domains are considered. These domains arise in the problems of approximation by polyanalytic functions. Several analytic and geometric properties (both new and earlier known) of Nevanlinna domains are described. In particular, a new method for constructing Nevanlinna domains with boundaries belonging to the class

C^{1}

$\mathrm C^1$ is proposed, and new examples of such domains whose boundaries do not belong to the class

C^{1, α}

$\mathrm C^{1,\alpha }$ for

α \in (0, 1)

$\alpha \in (0,1)$ are presented. This method is based on the property of pseudocontinuation of a conformal mapping from the unit disk onto a Nevanlinna domain.

Received in December 2005

English version:
Proceedings of the Steklov Institute of Mathematics, 2006, Volume 253, Pages 186–194
DOI: https://doi.org/10.1134/S0081543806020155

Bibliographic databases:

UDC: 517.54+517.538

Language: Russian

Citation: K. Yu. Fedorovskiy, “On Some Properties and Examples of Nevanlinna Domains”, Complex analysis and applications, Collected papers, Trudy Mat. Inst. Steklova, 253, Nauka, MAIK «Nauka/Inteperiodika», M., 2006, 204–213; Proc. Steklov Inst. Math., 253 (2006), 186–194

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tm93

https://www.mathnet.ru/eng/tm/v253/p204

This publication is cited in the following 23 articles:

Astamur Bagapsh, Konstantin Fedorovskiy, Maksim Mazalov, “On Dirichlet problem and uniform approximation by solutions of second-order elliptic systems in R2”, Journal of Mathematical Analysis and Applications, 531:1 (2024), 127896
M. Ya. Mazalov, P. V. Paramonov, K. Yu. Fedorovskiy, “Criteria for $C^m$ -approximability of functions by solutions of homogeneous second-order elliptic equations on compact subsets of $\mathbb{R}^N$ and related capacities”, Russian Math. Surveys, 79:5 (2024), 847–917
Konstantin Fedorovskiy, Fields Institute Communications, 87, Function Spaces, Theory and Applications, 2023, 207
St. Petersburg Math. J., 34:3 (2023), 497–514
Vardakis D., Volberg A., “Free Boundary Problems in the Spirit of Sakai'S Theorem”, C. R. Math., 359:10 (2021), 1233–1238
Belov Yu., Borichev A., Fedorovskiy K., “Nevanlinna Domains With Large Boundaries”, J. Funct. Anal., 277:8 (2019), 2617–2643
Yu. S. Belov, K. Yu. Fedorovskiy, “Model spaces containing univalent functions”, Russian Math. Surveys, 73:1 (2018), 172–174
M. Ya. Mazalov, “On Nevanlinna domains with fractal boundaries”, St. Petersburg Math. J., 29:5 (2018), 777–791
Baranov A.D. Fedorovskiy K.Yu., “On l (1)-Estimates of Derivatives of Univalent Rational Functions”, J. Anal. Math., 132 (2017), 63–80
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
E. V. Borovik, K. Yu. Fedorovskiy, “On the Relationship Between Nevanlinna and Quadrature Domains”, Math. Notes, 99:3 (2016), 460–464
Baranov A.D., Carmona J.J., Fedorovskiy K.Yu., “Density of certain polynomial modules”, J. Approx. Theory, 206:SI (2016), 1–16
M. Ya. Mazalov, “An example of a non-rectifiable Nevanlinna contour”, St. Petersburg Math. J., 27:4 (2016), 625–630
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
Proc. Steklov Inst. Math., 279 (2012), 215–229
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 Mathematical Soc, 2012, 323–329
A. D. Baranov, K. Yu. Fedorovskiy, “Boundary regularity of Nevanlinna domains and univalent functions in model subspaces”, Sb. Math., 202:12 (2011), 1723–1740
Fedorovskiy K.Yu., “ $C^m$ -approximation by polyanalytic polynomials on compact subsets of the complex plane”, Complex Anal. Oper. Theory, 5:3 (2011), 671–681
Baranov A., Chalendar I., Fricain E., Mashreghi J., Timotin D., “Bounded symbols and reproducing kernel thesis for truncated Toeplitz operators”, J. Funct. Anal., 259:10 (2010), 2673–2701
Fedorovskiy K.Yu., “Nevanlinna domains in problems of polyanalytic polynomial approximation”, Analysis and mathematical physics, Trends Math., Birkhäuser, Basel, 2009, 131–142

Citing articles in Google Scholar: Russian citations, English citations
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Труды Математического института имени В. А. Стеклова

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