Geodesic
On entire functions with given asymptotic behavior
Problemy analiza, Tome 7 (2018) no. 3, pp. 12-30 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study approximation of subharmonic functions on the complex plane by logarithms of moduli of entire functions. In the theory of series of exponentials these entire functions are the main tool. In questions of decomposition of functions into a series of exponentials, the subharmonic function, as a rule, satisfies the Lipschitz condition. We prove the theorem on approximation of such subharmonic functions. Also we prove the theorem on joint approximation of two subharmonic functions.
Keywords: subharmonic function, approximation, entire function, Riesz measure. 
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K. P. Isaev. On entire functions with given asymptotic behavior. Problemy analiza, Tome 7 (2018) no. 3, pp. 12-30. http://geodesic.mathdoc.fr/item/PA_2018_7_3_a1/

[1] Azarin V. S., “On rays of completely regular growth of an entire function”, Math. USSR-Sb., 8:4 (1985), 437–450. DOI | DOI

[2] Isaev K. P., Trounov K. V., Yulmukhametov R. S., “Representation of functions in locally convex subspaces of $A^ \infty (D)$ by series of exponentials”, Ufa Math. Journal, 9:3 (2017), 48–60 | DOI | MR

[3] Lutsenko V. I., Yulmukhametov R. S., “On the accuracy of asymptotic approximation of subharmonic functions by the logarithm of the modulus of an entire function”, Ufimsk. Mat. Zh., 2:3 (2010), 46–53 (Russian) | MR | Zbl

[4] Lyubarskii Yu. I., Sodin M. L., Analogues of Sine Type Function for Convex Domains, Preprint No 17, Institute for Low Temperatures, Ukrainian Acad. Sci., Kharkov, 1986 (Russian) | MR

[5] Lyubarskii Y., Malinnikova E. J., “On approximation of subharmonic functions”, J. Anal. Math., 83:121 (2001), 257–282 | DOI | MR

[6] Napalkov V. V., “Spaces of analytic functions of prescribed growth near the boundary”, Math. USSR-Izv., 30:2 (1988), 263–281 | DOI | MR | Zbl

[7] Ronkin L. I., Vvedenie v teoriyu tselykh funktsii mnogikh peremennykh, Nauka, M., 1971 (Russian)

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