Hostname: page-component-669899f699-swprf Total loading time: 0 Render date: 2025-04-27T09:18:17.813Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Ahern, P., Flores, M. and Rudin, W., ‘An invariant volume mean value property’, J. Funct. Anal. 111 (1993), 380–397.CrossRefGoogle Scholar
[2]Derriennic, Y., ‘Lois ≫ zéro ou deux ≪ pour les processus de Markov’, Ann. Inst. Henri Poincaré XII (1976), 111–129.Google Scholar
[3]Helgason, S., Topics in harmonic analysis on homogeneous spaces (Birkhäuser, Boston, MA, 1981).Google Scholar
[4]Helgason, S., Groups and geometric analysis. Integral geometry, invariant differential operators and spherical functions, Pure and Applied Mathematics 113 (Academic Press, Orlando, FL, 1984).Google Scholar
[5]Katznelson, Y. and Tzafriri, L., ‘On power bounded operators’, J. Funct. Anal. 68 (1986), 313–328.CrossRefGoogle Scholar
[6]Lee, J., ‘The iteration of the Berezin transform in the polydisc’, Complex Variables Theory Appl. (to appear).Google Scholar
[7]Rudin, W., Function theory in the unit ball of Cn (Springer-Verlag, Berlin, Heidelberg, New York, 1980).CrossRefGoogle Scholar