Orthogonal Polynomials, Verblunsky Coefficients, and a Szegő-Verblunsky Theorem on the Unit Sphere in ${\mathbb{C}}^d$

Connor J. Gauntlett, David P. Kimsey

Given a measure $\hat{I}¼$ on the unit sphere $\partial {\mathbb{B}}^d$ in ${\mathbb{C}}^d$ with Lebesgue decomposition $\mathrm{d}\hat{I}¼=w\mathrm{d}\ddot{I}ƒ+\mathrm{d}\hat{I}{¼}_s$, with respect to the rotati…