Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A mean value theorem
on bounded symmetric domains


Author: Miroslav Englis
Journal: Proc. Amer. Math. Soc. 127 (1999), 3259-3268
MSC (1991): Primary 31C05, 32M15; Secondary 31B10
Published electronically: May 4, 1999
MathSciNet review: 1625737
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $\Omega $ be a Cartan domain of rank $r$ and genus $p$ and $B_\nu$, $\nu >p-1$, the Berezin transform on $\Omega $; the number $B_{\nu }f(z)$ can be interpreted as a certain invariant-mean-value of a function $f$ around $z$. We show that a Lebesgue integrable function satisfying $f=B_\nu f=B_{\nu +1}f=\dots =B_{\nu +r}f$, $\nu \ge p$, must be $\mathcal{M}$-harmonic. In a sense, this result is reminiscent of Delsarte's two-radius mean-value theorem for ordinary harmonic functions on the complex $n$-space $\mathbf{C}^{n}$, but with the role of radius $r$ played by the quantity $1/\nu $.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 31C05, 32M15, 31B10

Retrieve articles in all journals with MSC (1991): 31C05, 32M15, 31B10


Additional Information

Miroslav Englis
Affiliation: MÚ AV ČR, Žitná 25, 11567 Prague 1, Czech Republic
Email: englis@math.cas.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05052-2
PII: S 0002-9939(99)05052-2
Keywords: Berezin transform, bounded symmetric domains, invariant mean-value property
Received by editor(s): January 28, 1998
Published electronically: May 4, 1999
Additional Notes: The author’s research was supported by GA AV ČR grant A1019701 and by GA ČR grant 201/96/0411.
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1999 American Mathematical Society