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Universal functions in several complex variables

Published online by Cambridge University Press:  09 April 2009

P. S. Chee
P. S. Chee
Affiliation:
Department of Mathematics University of MalayaKuala Lumpur Malaysia
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Abstract

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It is proved that there exists a universal good inner function in the open unit polydisc Un, that is its non Euclidean translates are dense in the closed unit ball of H∞ (Un) and that there exists a universal function in the open unit ball Bn of Cn. These generalize Heins' result on universal Blaschke products.

1980 Mathematics subject classification (Amer. Math. Soc.): primary 32 A 10.

Keywords

Polydiscballholomorphic automorphismbounded holomporphic functionuniversal Blaschke productuniversal inner function.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 2 , September 1979 , pp. 189 - 196
Copyright
Copyright © Australian Mathematical Society 1979

References

Birkhoff, G. D. (1929), ‘Demonstration d'un théorème élémentaire sur les fonctions entières’, Comptes Rendus Acad. Sci. Paris 189, 473–475.Google Scholar
Curtis, P. C. Jr (1969), Peak points for algebras of analytic functions’, J. Functional Analysis 2, 35–47.CrossRefGoogle Scholar
Heins, M. (1955), ‘A universal Blachke product’, Archiv der Math. 6, 41–44.CrossRefGoogle Scholar
Markushevich, A. I. (1965), Theory of functions of a complex varibale, Vol. I (Prentice-Hall, Englewood Cliffis, N. J.).Google Scholar
Rudin, W. (1969), Function theory in polydiscs (W. A. Benjamin, New York).Google Scholar
Seidel, W. and Walsh, J. L. (1941), ‘On approximation by Euclidean and non-Euclidean translations of an analystic function,’ Bull. Amer. Math. Soc. 47, 916–920.CrossRefGoogle Scholar