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arXiv · 2510.16667

A Haagerup inequality through the use of orthogonal polynomials

Félix Parraud
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Abstract

In this paper we prove that the Haagerup inequality for non-homogeneous polynomials in free semicircular variables of degree $n$ is optimal with a constant of order $n^{3/2}$. We also show an operator valued Haagerup inequality which improves on existing results. Our main tool to do so are free Chebyshev polynomials also known as $0$-Hermite polynomials.

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Félix Parraud. 2025-10-18. A Haagerup inequality through the use of orthogonal polynomials. https://arxiv.org/abs/2510.16667

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