A theory of orthogonal polynomials on the quaternionic sphere is introduced via q-positive measures, extending the Szegő–Verblunsky and Baxter theorems with new matrix-valued Schur recurrences and Verblunsky formulas.
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Orthogonal Polynomials, a Szeg\H{o}--Verblunsky Theorem and Baxter's Theorem on the Quaternionic Sphere
A theory of orthogonal polynomials on the quaternionic sphere is introduced via q-positive measures, extending the Szegő–Verblunsky and Baxter theorems with new matrix-valued Schur recurrences and Verblunsky formulas.