Book Review: Entire holomorphic mappings in one and several complex variables

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Some inequalities in connection to relative orders of entire functions of several complex variables

Let f, g and h be all entire functions of several complex variables. In this paper we would like to establish some inequalities on the basis of relative order and relative lower order of f with respect to g when the relative orders and relative lower orders of both f and g with respect to h are given.

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On Identical Vanishing of Holomorphic Functions in Several Complex Variables.

We will make some comment on the following recent result of J. J. Kohn. In the complex space Cn:(z1, . . . , zn) if fl, . . . , fn are holomorphic in the unit ball and have continuous boundary values on the boundary, and if on the boundary the linear combination 1fi+ + j,,f is 0, then the functions fl, . .. , f,, are identically 0. 1. We denote by D any bounded circular domain in C., by B its b...

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Kernel Convergence and Biholomorphic Mappings in Several Complex Variables

We deal with kernel convergence of domains in Cn which are biholomorphically equivalent to the unit ball B. We also prove that there is an equivalence between the convergence on compact sets of biholomorphic mappings on B, which satisfy a growth theorem, and the kernel convergence. Moreover, we obtain certain consequences of this equivalence in the study of Loewner chains and of starlike and co...

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Inequalities for Holomorphic Functions of Several Complex Variables

Sharp norm-inequalities, valid for functional Hilbert spaces of holomorphic functions on the polydisk, unit ball and C" are established by using the notion of reproducing kernels. These inequalities extend earlier results of Saitoh and ours.

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Global Holomorphic Functions in Several Noncommuting Variables

We define a free holomorphic function to be a function that is locally a bounded nc-function. We prove that free holomorphic functions are the functions that are locally uniformly approximable by free polynomials. We prove a realization formula and an OkaWeil theorem for free analytic functions.

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ژورنال

عنوان ژورنال: Bulletin of the American Mathematical Society

سال: 1977

ISSN: 0002-9904

DOI: 10.1090/s0002-9904-1977-14330-9