Noncommutative transforms and free pluriharmonic functions

Details Noncommutative transforms and free pluriharmonic functions Noncommutative transforms and free pluriharmonic functions

2007-01-24

arxiv.org/abs/math/0701682v4

Adv. Math. 220 (2009), 831-893

Mathematics

Functional Analysis

46 pages

Scientific paper

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.

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