– Europe/Lisbon — Online
Room P3.10, Mathematics Building
Lisbon WADE — Webinar in Analysis and Differential Equations
Gevorg Mnatsakanyan, Institute of Mathematics, National Academy of Sciences of Armenia.
Baxter's theorem and possibilities of its quantitative variants.
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 $\ell^1$. We prove an analog of Baxter's theorem for the SU(2)-valued nonlinear Fourier transform. The proof of Baxter's theorem is qualitative in nature. We explore possible formulations of such quantitative theorems with norm and Lipschitz estimates. In particular, we construct a counterexample for certain such estimates