Some properties of Reinhardt and Hartogs domains
DOI:
https://doi.org/10.5902/2179460X27130Keywords:
several complex variables, Reinhardt domain, Hartogs domain, convexityAbstract
The domains of certain types, such as Reinhardt and Hartogs, are used in different problems of theory of functions of several complex variables. For instance, any power series of several complex variables converges in the complete logarithmically convex Reinhardt domain. Transformations of Reinhardt and Hartogs allow us to diminish the dimension of space and to consider some type of domains using its images. This allows the visibility of the geometric representation and the simplification of the study of properties of such domains. In this article we consider some properties of Reinhardt and Hartogs domains and transformations. The properties of domain conservation under Reinhardt transformation and convexity conservation under Reinhardt and Hartogs transformation are proved.
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References
H. Cartan, Elementary Theory of Analytic Functions of One or Several Complex Variables. New York, Dover Pub., 1995, 226p.
L. Hormander, An Introduction to Complex Analysis in Several Variables. Amsterdam, North-Holland, 1990, 254p.
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M.R. Range, Holomorphic Functions and Integral Representations in Several Complex Variables. New York, Springer-Verlag, 1998, 388p.
W. Rudin, Principies of Mathematical Analysis. New York, McGraw-Hill, 1976, 342p.
B.v. Shabat, Introduction to Complex Analysis. Part 2: Functions of Several Variables. Providence, American Mathematical Society, 1992, 381p
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