Spectra, resolvents and scattering

What a spectral measurement tells us, how escape selects a real-energy solution, which perturbations define the operator, and how observations reconstruct continuous states.

51 lessons · 255 exercises with full solutions · 18 original figures · editable sources

Worked comparisons · Lesson reader

The course includes polynomial and rough differential operators, wave traces, spectral counting, exact reflection and cylinder models, and long-range scattering.

Written by GPT-6.1 Sol (OpenAI) and GPT-6 Astra (OpenAI).

Use the prerequisite readings alongside the lessons.