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 Tr. Mat. Inst. Steklova, 2001, Volume 235, Pages 262–271 (Mi tm247)

Approximation and Boundary Properties of Polyanalytic Functions

K. Yu. Fedorovskiy

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

Abstract: We give a review of some recent results concerning the uniform approximation of functions by polyanalytic functions and polyanalytic polynomials on planar compact sets. We discuss the boundary properties of polyanalytic functions and their relationships with uniform approximation problems. Some problems of approximation by the solutions of homogeneous second-order elliptic equations with constant complex coefficients are also considered.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2001, 235, 251–260

Bibliographic databases:
UDC: 517.5

Citation: K. Yu. Fedorovskiy, “Approximation and Boundary Properties of Polyanalytic Functions”, Analytic and geometric issues of complex analysis, Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin, Tr. Mat. Inst. Steklova, 235, Nauka, MAIK «Nauka/Inteperiodika», M., 2001, 262–271; Proc. Steklov Inst. Math., 235 (2001), 251–260

Citation in format AMSBIB
\Bibitem{Fed01} \by K.~Yu.~Fedorovskiy \paper Approximation and Boundary Properties of Polyanalytic Functions \inbook Analytic and geometric issues of complex analysis \bookinfo Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin \serial Tr. Mat. Inst. Steklova \yr 2001 \vol 235 \pages 262--271 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm247} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1886586} \zmath{https://zbmath.org/?q=an:1001.30030} \transl \jour Proc. Steklov Inst. Math. \yr 2001 \vol 235 \pages 251--260 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. K. Yu. Fedorovskiy, “On Some Properties and Examples of Nevanlinna Domains”, Proc. Steklov Inst. Math., 253 (2006), 186–194
2. Fedorovskiy K.Yu., “Nevanlinna Domains in Problems of Polyanalytic Polynomial Approximation”, Analysis and Mathematical Physics, Trends in Mathematics, 2009, 131–142
3. A. D. Baranov, K. Yu. Fedorovskiy, “Boundary regularity of Nevanlinna domains and univalent functions in model subspaces”, Sb. Math., 202:12 (2011), 1723–1740
4. 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
5. M. Ya. Mazalov, “An example of a non-rectifiable Nevanlinna contour”, St. Petersburg Math. J., 27:4 (2016), 625–630
6. M. Ya. Mazalov, “On Nevanlinna domains with fractal boundaries”, St. Petersburg Math. J., 29:5 (2018), 777–791
7. Baranov A.D., Fedorovskiy K.Yu., “On l (1)-Estimates of Derivatives of Univalent Rational Functions”, J. Anal. Math., 132 (2017), 63–80
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