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 $\mu$ on the unit sphere $\partial {\mathbb{B}}^d$ in ${\mathbb{C}}^d$ with Lebesgue decomposition $\mathrm{d}\mu =w\mathrm{d}\sigma +\mathrm{d}{\mu }_s$, with respect to the rotation-i…