Year: 2026
Type: preprint
Abstract: These lectures are aimed at junior researchers seeking to enter the field of applications of complex analysis to harmonic analysis, Fourier analysis, spectral and scattering theory for differential operators and related fields. Starting with classical completeness problems posed by Bernstein, Beurling and Malliavin, Wiener, Kolmogorov and Krein, the course progresses to the solutions of the Gap and Type Problems, inverse spectral problems for Schrödinger operators and canonical Hamiltonian systems, and pointwise convergence of the non-linear Fourier transform. Each lecture is supplemented with exercises and references.
Source: arXiv (Cornell University)
Author: Poltoratski, Alexei
Institution: University of Wisconsin–Madison
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204883117