The Spectral Theorem for Compact Self-Adjoint Operators (IFA21 Video 19)

Complete lecture notes and slides of the lecture are available at: https://paunonenmath.com/teaching.html Topics of the lecture: The Spectral Theorem for compact self-adjoint operators on a Hilbert space Construction of the spectral decomposition and the proof of the Spectral Theorem Representing the solutions of linear operator equations using the spectral decomposition Application: Solution of the Fredholm integral equation (of the second kind) with a separable kernel. Part of the online course "Introduction to Functional Analysis" at Tampere University, January--February 2021 (Week 7, Video 19). Full "Introduction to Functional Analysis" series (19 videos):    • Introduction to Functional Analysis video ...   Lecture given by Lassi Paunonen (Associate professor in Mathematics, https://paunonenmath.com/)