PreprintCC BY 4.0arXiv
Complex Analysis in completeness, spectral and scattering problems
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.
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BibTeX
@misc{poltoratski2026complex,
title = {{Complex Analysis in completeness, spectral and scattering problems}},
author = {Alexei Poltoratski},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28801},
eprint = {2608.28801},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28801},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Complex Analysis in completeness, spectral and scattering problems
AU - Alexei Poltoratski
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28801
UR - https://arxiv.org/abs/2608.28801
AB - 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.
ER -