M. Ya. Mazalov, “Uniform Approximation of Functions Continuous on a Compact Subset of $\mathbb C$ and Analytic in Its Interior by Functions Bianalytic in Its Neighborhoods”, Mat. Zametki, 69:2 (2001), 245–261; Math. Notes, 69:2 (2001), 216

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Matematicheskie Zametki, 2001, Volume 69, Issue 2, Pages 245–261
DOI: https://doi.org/10.4213/mzm500 (Mi mzm500)

This article is cited in 6 scientific papers (total in 6 papers)

Uniform Approximation of Functions Continuous on a Compact Subset of

$\mathbb C$ and Analytic in Its Interior by Functions Bianalytic in Its Neighborhoods

M. Ya. Mazalov

Military Academy of Air Defence Forces of Russia Federation

Full-text PDF (301 kB) Citations (6)

References:

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DOI: https://doi.org/10.4213/mzm500

Abstract: We prove that an arbitrary function continuous on a compact set

$X\subset\mathbb C$ and holomorphic in the interior of

$X$ can be approximated by functions bianalytic in neighborhoods of

$X$ with arbitrary accuracy.

Received: 19.06.2000
Revised: 09.08.2000

English version:
Mathematical Notes, 2001, Volume 69, Issue 2, Pages 216–231
DOI: https://doi.org/10.1023/A:1002876419788

Bibliographic databases:

UDC: 517

Language: Russian

Citation: M. Ya. Mazalov, “Uniform Approximation of Functions Continuous on a Compact Subset of

$\mathbb C$ and Analytic in Its Interior by Functions Bianalytic in Its Neighborhoods”, Mat. Zametki, 69:2 (2001), 245–261; Math. Notes, 69:2 (2001), 216–231

Citation in format AMSBIB

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\jour Mat. Zametki

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\pages 245--261

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\elib{https://elibrary.ru/item.asp?id=13361641}

\transl

\jour Math. Notes

\yr 2001

\vol 69

\issue 2

\pages 216--231

\crossref{https://doi.org/10.1023/A:1002876419788}

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Linking options:

https://www.mathnet.ru/eng/mzm500

https://doi.org/10.4213/mzm500

https://www.mathnet.ru/eng/mzm/v69/i2/p245

This publication is cited in the following 6 articles:

Sorin G. Gal, Irene Sabadini, “Density of Complex and Quaternionic Polyanalytic Polynomials in Polyanalytic Fock Spaces”, Complex Anal. Oper. Theory, 18:1 (2024)
Gal S.G. Sabadini I., “Approximation By Convolution Polyanalytic Operators in the Complex and Quaternionic Compact Unit Balls”, Comput. Methods Funct. Theory, 2022
Zoubeir H., Kabbaj S., “On the Representation and the Uniform Polynomial Approximation of Polyanalytic Functions of Gevrey Type on the Unit Disk”, Iran. J. Math. Sci. Inform., 16:2 (2021), 89–115
M. Ya. Mazalov, “A criterion for uniform approximability on arbitrary compact sets for solutions of elliptic equations”, Sb. Math., 199:1 (2008), 13–44
M. Ya. Mazalov, “Uniform approximations by bianalytic functions on arbitrary compact subsets of $\mathbb C$”, Sb. Math., 195:5 (2004), 687–709
K. Yu. Fedorovskiy, “Approximation and Boundary Properties of Polyanalytic Functions”, Proc. Steklov Inst. Math., 235 (2001), 251–260

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

Statistics & downloads:
Abstract page:	523
Full-text PDF :	216
References:	72
First page:	2

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