David P. Kimsey

collaborators

3 papers

math.CA2026

Orthogonal Polynomials, a SzegÅ--Verblunsky Theorem and Baxter's Theorem on the Quaternionic Sphere

Connor J. Gauntlett, David P. Kimsey

We introduce a theory of orthogonal polynomials on the unit sphere of the quaternions based on the notion of a $q$ -positive measure (which originated in a work of Alpay, Colombo, t…

math.CV2025

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

Connor J. Gauntlett, David P. Kimsey

Given a measure $I^¼$ on the unit sphere $\partial B^{d}$ in $C^{d}$ with Lebesgue decomposition $d I^¼ = w d I ¨ + d I^¼_{s}$ , with respect to the rotati…

math.FA2025

A Noncommutative SzegÅ-Type Theorem on the Row-Ball

Connor J. Gauntlett, David P. Kimsey

In this paper we leverage the recently developed theory of noncommutative (nc) measures to prove a free noncommutative analogue of many known equalities extending the weak SzegÅ l…

Orthogonal Polynomials, a SzegÅ--Verblunsky Theorem and Baxter's Theorem on the Quaternionic Sphere

Orthogonal Polynomials, Verblunsky Coefficients, and a SzegÅ-Verblunsky Theorem on the Unit Sphere in Cd

A Noncommutative SzegÅ-Type Theorem on the Row-Ball

Orthogonal Polynomials, a SzegÅ--Verblunsky Theorem and Baxter's Theorem on the Quaternionic Sphere

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

A Noncommutative SzegÅ-Type Theorem on the Row-Ball