Lecture 15: Orthonormal Bases and Fourier Series

MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=Yb69dAq4uh8&list=PLUl4u3cNGP63micsJp_--fRAjZXPrQzW_&index=15 We prove some important identities for Hilbert spaces, such as the Fourier-Bessel series and Parseval’s identity. We explore a close connection to Fourier analysis, defining Fourier coefficients, series and the Cesaro-Fourier mean. License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu Support OCW at http://ow.ly/a1If50zVRlQ We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.