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Functions invariant under the Bochner–Martinelli integral

Published online by Cambridge University Press:  17 April 2009

Jaesung Lee
Jaesung Lee
Affiliation:
Department of Mathematics, Sogang University, Seoul 121–742, Korea e-mail: jalee@sogang.ac.kr
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Abstract

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We give an elementary proof of the statement that a function f on the closed unit ball of Cn, integrable on the unit sphere, is holomorphic if it is invariant under the Bochner–Martinelli integral transform.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 1 , February 2002 , pp. 55 - 57
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Romanov, A., ‘Spectral analysis of the Martinelli–Bochner operator for the ball in Cn and its application’, Funct. Anal. Appl. 12 (1978), 232–234.CrossRefGoogle Scholar
[2]Rudin, W., Function theory in the unit ball of Cn (Springer-Verlag, Berlin, Heidelberg, New York, 1980).CrossRefGoogle Scholar