Point evaluation and Hardy space on a homogeneous tree

Carleson Measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on Complex Balls

We characterize the Carleson measures for the Drury-Arveson Hardy space and other Hilbert spaces of analytic functions of several complex variables. This provides sharp estimates for Drury's generalization of Von Neumann's inequality. The characterization is in terms of a geometric condition, the "split tree condition", which reflects the nonisotropic geometry underlying the Drury-Arveson Hardy space.

Positive definite radial kernels on homogeneous trees and products

We give a new proof of a classical result which provides a one-to-one correspondence between positive definite radial kernels on a homogeneous tree and finite Borel measures on the interval $[-1,1]$. Our methods allow us to find a new characterisation in terms of positive trace-class operators on $\ell_2$. Furthermore, we extend both characterisations to finite products of homogeneous trees. The proof relies on a formula for the norm of radial Schur multipliers, in the spirit of Haagerup--Steenstrup--Szwarc, and a variation of the Hamburger moment problem.

管状划分与齐次有根树的量子自同构群的表示

Tubular partitions and representations of the quantum automorphism group of a homogeneous rooted tree

本文引入管状划分的刚性张量范畴，为齐次有根树的量子自同构群的表示范畴提供组合模型。