Abstract
We construct different extensions of functions subharmonic in a half plane to the whole plane. The results obtained are applied to the approximation of subharmonic functions of finite order in a half plane by the logarithm of the modulus of an entire function. It is shown that the problem of extension of a plurisubharmonic function may have no solution.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 8, pp. 1017–1030, August, 1994.
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Rashkovskii, A.Y., Ronkin, L.I. Extension and approximation of functions subharmonic in a half plane. Impossibility of extension of plurisubharmonic functions. Ukr Math J 46, 1117–1130 (1994). https://doi.org/10.1007/BF01056173
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DOI: https://doi.org/10.1007/BF01056173