The Two-Parameter Free Unitary Segal-Bargmann Transform and its Biane-Gross-Malliavin Identification
Probability
2016-09-05 v2 Functional Analysis
Operator Algebras
Abstract
Motivated by the two-parameter free unitary Segal-Bargmann transform in the form of conditional expectation, we derive the integral transform representation of the two-parameter free unitary Segal-Bargmann transform which coincides to the large- limit of the two-parameter Segal-Bargmann transform on the unitary group and explore its limiting behavior. We also extend the notion of circular systems in order to define a two-parameter free Segal-Bargmann transform and prove a version of Biane-Gross-Malliavin Theorem of the two-parameter free unitary Segal-Bargmann transform.
Keywords
Cite
@article{arxiv.1601.03182,
title = {The Two-Parameter Free Unitary Segal-Bargmann Transform and its Biane-Gross-Malliavin Identification},
author = {Ching-Wei Ho},
journal= {arXiv preprint arXiv:1601.03182},
year = {2016}
}