Titlebook: Selected Topics in Complex Analysis; The S. Ya. Khavinson Vladimir Ya. Eiderman,Mikhail V. Samokhin Book 2005 Birkh?user Basel 2005 Complex

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,Generalization of Carathéodory’s Inequality and the Bohr Radius for Multidimensional Power Series,s holomorphic in the unit disk in C, this generalization of Carathéodory’s inequality implies the classical inequalities of Carahtéodory and Landau. As an application, new results on multidimensional analogues of Bohr’s theorem on power series are obtained. Furthermore, the estimate from below of Bo

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On , Spaces in the Half-Plane,aces can have arbitrary growth near the finite points of the real axis. The canonical representations of functions from these classes are established by an approach based on the use of Fourier-Laplace transform apparatus.

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Extremal Problems for Nonvanishing Functions in Bergman Spaces,space, and in fact must be bounded. We conjecture what the exact form of the extremal function is. Finally, we discuss the specific problem of minimizing the norm of non-vanishing Bergman functions whose first two Taylor coefficients are given.