3 papers
math.CV2026
A maximal estimate for the non-linear Fourier transform
Alexei Poltoratski
We discuss estimates for the maximal operator associated with the non-linear Fourier transform of an -function on the half-line. For potentials with bounded dyadic masse…
math.CV2025
Pointwise convergence of the non-linear Fourier transform
Alexei Poltoratski
We prove pointwise convergence for the scattering data of a Dirac system of differential equations. Equivalently, we prove an analog of Carleson's theorem on almost everywhere conv…
math.CV2025
Etudes in the inverse spectral problem, II
Nikolai Makarov, Alexei Poltoratski
We apply the approach developed in our previous papers to obtain examples of solutions to the inverse spectral problem (ISP) for the canonical Hamiltonian system. One of our goals…