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

This article is cited in 7 scientific papers (total in 7 papers)

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
Received in May 2001

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
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    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  mathnet  crossref  mathscinet  elib
    2. Fedorovskiy K.Yu., “Nevanlinna Domains in Problems of Polyanalytic Polynomial Approximation”, Analysis and Mathematical Physics, Trends in Mathematics, 2009, 131–142  mathscinet  zmath  isi
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. 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
    6. M. Ya. Mazalov, “On Nevanlinna domains with fractal boundaries”, St. Petersburg Math. J., 29:5 (2018), 777–791  mathnet  crossref  mathscinet  isi  elib
    7. 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
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