Some Questions of the Nevanlinna Theory for the Complex Half-Plane |
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Authors: | M. A. Fedorov A. F. Grishin |
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Affiliation: | (1) Department of Mathematics and Mechanics, Kharkov State University, 310077 Kharkov, Ukraine |
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Abstract: | In this paper we give variants of the logarithmic derivative lemma and the second main theorem for the complex half-plane. Here the second main theorem is a special case of a theorem concerning polynomial functions of the coordinates of a holomorphic curve f : C+ Pn. This theorem is a variant for C+ of a theorem of A. Eremenko and M. Sodin, who considered an entire curve f : C+ Pn. The proofs are realized because of the introduction of natural classes of subharmonic, -subharmonic, holomorphic, meromorphic functions in C+ . Such functions we shall call just functions. |
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Keywords: | integrated and nonintegrated form of the second main theorem just subharmonic function in C+ logarithmic derivative lemma |
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