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arXiv · 2610.01711

Quantitative possibilities for Baxter's theorem in nonlinear Fourier analysis

Michel Alexis·Gevorg Mnatsakanyan·Kristina Oganesyan
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Abstract

Baxter's classical theorem for orthogonal polynomials on the unit circle establishes that the linear Fourier coefficients of a measure are in $\ell^1$ if and only if the nonlinear coefficients, i.e., the so-called Verblunsky coefficients, are in $\ell^1$. However, this equivalence is purely qualitative. We explore possible formulations of such quantitative theorems with norm and Lipschitz estimates for the $SU(2)$-valued nonlinear Fourier transform, for which the analog of Baxter's theorem has been recently obtained. In particular, the highlight of this paper is a number-theoretic construction for the NLFT which proves some negative results in this direction. We also prove a positive result and discuss the limitations of Baxter's method.

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Michel Alexis, Gevorg Mnatsakanyan, Kristina Oganesyan. 2026-10-01. Quantitative possibilities for Baxter's theorem in nonlinear Fourier analysis. https://arxiv.org/abs/2610.01711

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