Planar Lebesgue measure of exceptional set in approximation of subharmonic functions
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (2009), pp. 347-358.

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We consider the pointwise approximation of a subharmonic function having finite order by the logarithm of the modulus of an function up to a bounded quantity. We prove an estimate from below of the planar Lebesgue measure of the exceptional Set in such approximation.
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Markiyan Girnyk. Planar Lebesgue measure of exceptional set in approximation of subharmonic functions. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (2009), pp. 347-358. http://geodesic.mathdoc.fr/item/JMAG_2009_5_a1/

[1] S. N. Mergelyan, “Uniform Approximations of Functions of Complex Variable”, Usp. Mat. Nauk, 7:2 (1952), 31–122 (Russian) | MR | Zbl

[2] A. Beurling, P. Malliavin, “On Fourier Transforms of Measures with Compact Support”, Acta Math., 107 (1962), 291–309 | DOI | MR | Zbl

[3] N. U. Arakelyan, “Entire Functions of Finite Order with Infinite Set of Deficiencies”, Dokl. AN SSSR, 170:5 (1966), 999–1002 (Russian) | MR | Zbl

[4] Yu. I. Lyubarskii, M. L. Sodin, Analogs of Sine-Type Functions for Convex Domains, Preprint 17-86, FTINT AN USSR, Kharkov, 1986 (Russian)

[5] P. Z. Agranovich, V. N. Logvinenko, “Many Term Asymptotic Representation of Function Subharmonic in the Plane”, Sib. Mat. J., 32:1 (1991), 3–21 (Russian) | MR | Zbl

[6] D. Drasin, “Approximation of Subharmonic Functions with Applications”, Approximation, Complex Analysis, and Potential Theory (Proc. NATO ASI. Montreal, Canada, 3–14 July 2000), Kluwer Acad. Publ., Dordrecht–Boston–London, 2001, 163–189 | DOI | MR | Zbl

[7] W. K. Hayman, P. B. Kennedy, Subharmonic Functions, v. 1, Acad. Press, London–New York–San Francisco, 1976 | MR

[8] A. A. Goldberg, I. V. Ostrovskii, Distribution of Values of Meromorphic Functions, Nauka, Moscow, 1970 (Russian) | MR

[9] I. E. Chyzhykov, “Approximation of Subharmonic Functions”, St. Petersburg Math. J., 16:3 (2004), 211–237 (Russian) | MR | Zbl

[10] Yu. Lyubarskii, Eu. Malinnikova, “On Approximation of Subharmonic Functions”, J. d'Analyse Math., 83 (2001), 121–149 | DOI | MR | Zbl

[11] R. S. Yulmukhametov, “Approximation of Subharmonic Functions”, Anal. Math., 11:3 (1985), 257–282 (Russian) | DOI | MR | Zbl

[12] M. Girnyk, “Accuracy of Approximation of Subharmonic Function by Logarithm of Modulus of Analytic One in Chebyshev Metric”, Zap. Nauch. Sem. POMI, 327 (2005), 55–73 (Russian) | MR | Zbl

[13] A. Edrei, W. H. J. Fuchs, “Bounds for the Number of Deficient Values of Certain Classes of Meromorphic Functions”, Proc. London Math. Soc., 12 (1962), 113–145 | DOI | MR