Wang, Jiun-Chau2016-09-222016-09-222016-092016-09-22Septemberhttp://hdl.handle.net/10388/7464In this thesis, we present a study of Voiculescu’s R-transform from the complex and harmonic analysis point of view. This study is based on the unpublished notes [4] of James Mingo and Roland Speicher, in which the main feature is the phenomenon of analytic subordination. Thus, this thesis is not an original research, but author’s own understanding (of the aforementioned book [4]) and comments on this particular topic in free harmonic analysis.application/pdffree convolution, R-transform addition formulaThesis2016-09-22