发表机构
University of Wisconsin（威斯康星大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文介绍面向青年研究者的复分析应用课程，涵盖经典完备性问题、谱与散射理论相关问题的求解，配有练习与参考文献，助力学习者进入相关研究领域。
AI 中文摘要
本课程面向有志进入复分析在调和分析、傅里叶分析、微分算子的谱与散射理论及相关领域应用的青年研究者开设。课程从Bernstein、Beurling、Malliavin、Wiener、Kolmogorov和Krein提出的经典完备性问题入手，逐步推进至间隙问题与型问题的求解、Schrödinger算子的逆谱问题、典型哈密顿系统以及非线性傅里叶变换的逐点收敛性，每讲均配有练习和参考文献。
英文摘要
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.
