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Properties of the Berezin transform of bounded functions

Published online by Cambridge University Press:  17 April 2009

Jaesung Lee
Jaesung Lee
Affiliation:
Global Analysis Research Center, Department of Mathematics, Seoul National University, Seoul 151–742, Korea
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Abstract

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We find the spectrum of the Berezin operator T on L∞(Bn), then we show that if f ∈ L∞(Bn) satisfies Sf = rf for some r in the unit circle, where S is any convex combination of the iterations of T, then f is M-harmonic.

Finally we decompose the subspace of L∞(Bn) where lim Tkf exists into the direct sum of two subspaces of L∞(Bn).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 1 , February 1999 , pp. 21 - 31
Copyright
Copyright © Australian Mathematical Society 1999

References

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