Geodesic
Approximation of Subharmonic Functions in the Half-Plane by the Logarithm of the Modulus of an Analytic Function
Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 483-492

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We approximate subharmonic functions defined in the open half-plane in the uniform metric outside the exceptional set by the logarithm of the modulus of an analytic (in the half-plane) function for the cases of a finite order and of an infinite lower order. We also obtain an estimate for the size of the exceptional set. It is shown that, in the case of a finite order, the obtained accuracy of the approximation cannot be essentially improved. 
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     author = {M. A. Hirnyk},
     title = {Approximation of {Subharmonic} {Functions} in the {Half-Plane} by the {Logarithm} of the {Modulus} of an {Analytic} {Function}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {483--492},
     publisher = {mathdoc},
     volume = {78},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_4_a0/}
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M. A. Hirnyk. Approximation of Subharmonic Functions in the Half-Plane by the Logarithm of the Modulus of an Analytic Function. Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 483-492. http://geodesic.mathdoc.fr/item/MZM_2005_78_4_a0/