Noncommutative transforms and free pluriharmonic functions

Abstract

In this paper, we study free pluriharmonic functions on noncommutative balls, and their boundary behavior. The main tools used in this study are certain noncommutative transforms which are introduced in the present paper and which generalize the classical transforms of Berezin, Poisson, Fantappie, Herglotz, and Cayley. Several classical results from complex analysis have free analogues in our noncommutative multivariable setting.

46 pages

Cited by in corpus (4)

• Free holomorphic automorphisms of the unit ball of $B(H{)}^n$
• Hyperbolic geometry on the unit ball of $B(H{)}^n$ and dilation theory
• Free holomorphic functions and interpolation
• Free pluriharmonic majorants and noncommutative interpolation