Mathematics – Complex Variables
Scientific paper
2011-05-13
Mathematics
Complex Variables
Scientific paper
The paper proposes a vector generalization of the basic concepts of the theory of complex variable: the concept of modulus and argument of complex number. The author introduces some generalizations of the notion of holomorphic functions and mappings to the case of infinite-dimensional complex spaces. This approach allows us to generalize several well-known results of geometric function theory to the case of infinite-dimensional complex spaces. In particular, the author summarizes a number of known theorems on the theory of functions of class S on infinite-dimensional complex space.
Bakhtin A. K.
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