Kozlova I. The Fourier series method for subharmonic functions in the half-plane.

In the thesis the criteria for affiliation delta-subharmonic function to the class of functions of finite -type in sene of Khabibullin are obtained. The analysis of the measures which are distributed in the upper half-plane is given, the measures which have finite -density are described . The notion of -admissibility of measure is introduced. For such measures the canonical function is constructed. Generalized representations of subharmonic functions of finite -type in half-plane in the sens of Rubel and in the sense of Nevanlinna are obtained. Analogue of Miles theorem for subharmonic function in C+ of infinite order with full measure on finite system of rays is obtained. It is proved that such function has also lower order infinity.