Logarithmically Convex Reinhardt Domains

Authors

DOI:

https://doi.org/10.5902/2179460X27233

Keywords:

Several complex variables, Reinhardt domain, logarithmic convexity

Abstract

The domains of certain types, such as Reinhardt ones, are important 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. In this article we prove the logarithmic convexity of complete convex Reinhardt domain.

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Author Biographies

Ludmila Bourchtein, Department of Mathematics, Pelotas State University, Campus Universitário da UFPel, Capão do Leão, Pelotas, RS.

Possui graduação em Bacharelado em matemática pela Universidade Federal do Leste Distante(1960), mestrado em Mestrado em matemática pura pela Universidade Federal do Leste Distante(1962) e doutorado em Doutorado em matemática pura pela Universidade Federal de São Petersburgo(1968). Atualmente é Pesquisador Associado da Universidade Federal de Pelotas. Tem experiência na área de Matemática, com ênfase em Análise.

Andrei Bourchtein, Department of Mathematics, Pelotas State University, Campus Universitário da UFPel, Capão do Leão, Pelotas, RS.

Possui graduação em Bacharelado em Matemática Aplicada pela Universidade Federal do Leste Distante(1982), mestrado em Mestrado em matematica aplicada pela Universidade Federal do Leste Distante(1984) e doutorado em Métodos numéricos da hidrodinâmica pelo Centro Hidrometeorológico da Rússia(1990). Atualmente é Professor Associado da Universidade Federal de Pelotas, referee da International journal for numerical methods in fluids, bolsista do Conselho Nacional de Desenvolvimento Científico e Tecnológico, Reviewer da American Mathematical Society e reviewer da Journal of Computational and Applied Mathematics. Tem experiência na área de Geociências, com ênfase em Meteorologia.

References

L. Bourchtein, A. Bourchtein, Some properties of Reinhardt and Hartogs Domains. UFSM, Ciencia e Natura, 2002, V.24, p.7-19.

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, 1973, 211p.

R. Narasimhan, Several Complex Variables. Chicago, University of Chicago Press, 1995, 174p.

B.V. Shabat, Introduction to Complex Analysis. Part 2: Functions of Several Variables. Providence, American Mathematical Society, 1992, 381p.

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Published

2003-12-09

How to Cite

Bourchtein, L., & Bourchtein, A. (2003). Logarithmically Convex Reinhardt Domains. Ciência E Natura, 25(25), 07–22. https://doi.org/10.5902/2179460X27233

Issue

CIÊNCIA E NATURA, V. 25, N. 25, 2003

Section

Articles

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