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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 ,...
Let be a bounded symmetric domain in and an irreducible arithmetic lattice which operates freely on . We prove that the cusp–compactification of is hyperbolic.
In 1945 the first author introduced the classes , 1 ≤ p<∞, α > -1, of holomorphic functions in the unit disk with finite integral
(1) ∬ |f(ζ)|p (1-|ζ|²)α dξ dη < ∞ (ζ=ξ+iη)
and established the following integral formula for :
(2) f(z) = (α+1)/π ∬ f(ζ) ((1-|ζ|²)α)/((1-zζ̅)2+α) dξdη, z∈ .
We have established that the analogues of the integral representation (2) hold for holomorphic functions in Ω from the classes , where:
1) , ;
2) Ω is the matrix domain consisting of those complex m...
Let D be a symmetric irreducible Siegel domain. Pluriharmonic functions satisfying a certain rather weak growth condition are characterized by r+2 operators (r+1 in the tube case), r being the rank of the underlying symmetric cone
The relationships between the JB*-triple structure of a complex spin factor S and the structure of the Hilbert space H associated to S are discussed. Every surjective linear isometry L of S can be uniquely represented in the form L(x) = mu.U(x) for some conjugation commuting unitary operator U on H and some mu belonging to C, |mu|=1. Automorphisms of S are characterized as those linear maps (continuity not assumed) that preserve minimal tripotents in S and the orthogonality relations among them.
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...
We realize closed geodesics on the real conformal compactification of the space V = Sym(2, ℝ) of all 2 × 2 real symmetric matrices as knots or 2-component links in and show that these knots or links have certain types of symmetry of period 2.
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