Remark on cyclic vectors in the Dirichlet space

Dirichlet Polyhedra for Cyclic Groups in Complex Hyperbolic Space

We prove that the Dirichlet fundamental polyhedron for a cyclic group generated by a unipotent or hyperbolic element y acting on complex hyperbolic «-space centered at an arbitrary point w is bounded by the two hypersurfaces equidistant from the pairs w, yw and w,y~lw respectively. The proof relies on a convexity property of the distance to an isometric flow containing y.

Bayesian Networks on Dirichlet Distributed Vectors

Exact Bayesian network inference exists for Gaussian and multinomial distributions. For other kinds of distributions, approximations or restrictions on the kind of inference done are needed. In this paper we present generalized networks of Dirichlet distributions, and show how, using the two-parameter Poisson-Dirichlet distribution and Gibbs sampling, one can do approximate inference over them....

The Dirichlet Space on the bi-disc

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Bilinear Forms on the Dirichlet Space

Hankel operators on the Hardy space of the disk, H (D) , can be studied as linear operators from H (D) to its dual space, as conjugate linear operators from H (D) to itself, or, in the viewpoint we will take here, as bilinear functionals on H (D) × H (D) . In that formulation, given a holomorphic symbol function b we consider the bilinear Hankel form, defined initially for f, g in P (D) , the s...