Spectrum of a Self-Adjoint Operator (IFA21 Video 17)

Complete lecture notes and slides of the lecture are available at: https://paunonenmath.com/teaching.html Topics of the lecture: The spectrum of a self-adjoint operator is real, and the residual spectrum is empty Relationship between the spectrum and the operator norm Orthogonality of eigenvectors corresponding to distinct eigenvalues Example: Computation of the eigenvalues of a Fredholm integral operator with a separable kernel Part of the online course "Introduction to Functional Analysis" at Tampere University, January--February 2021 (Week 7, Video 17). 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/)