Invariant inner product in spaces of holomorphic functions on bounded symmetric domains.
Let be a measure on a domain in such that the Bergman space of holomorphic functions in possesses a reproducing kernel and . The Berezin transform associated to is the integral operator The number can be interpreted as a certain mean value of around , and functions satisfying as functions having a certain mean-value property. In this paper we investigate the boundary behavior of , the existence of functions satisfying and having...
We define the Weyl functional calculus for real and complex symmetric domains, and compute the associated Weyl transform in the rank 1 case.
In an earlier paper, the first two authors have shown that the convolution of a function continuous on the closure of a Cartan domain and a -invariant finite measure on that domain is again continuous on the closure, and, moreover, its restriction to any boundary face depends only on the restriction of to and is equal to the convolution, in , of the latter restriction with some measure on uniquely determined by . In this article, we give an explicit formula for in terms of ,...
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