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Mirror symmetric polynomials orthogonal on the unit circle

Published 12 Oct 2025 in math.CA, math-ph, and math.MP | (2510.10447v1)

Abstract: We introduce and study a special family of polynomials orthogonal on the unit circle (OPUC). These OPUC satisfy a mirror symmetry property of their Verblunsky coefficients. Several equivalent conditions for the OPUC to be mirror symmetric are presented. Corresponding unitary CMV matrices satisfy simple algebraic relations similar to relations for persymmetric tridiagonal matrices. We present three explicit examples of mirror symmetric OPUC.

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