I have been writing my own lecture notes (based, of course, on an array of well known references and also on some of my notes from my graduate studies) for the course Advanced Analysis. I have decided to do this because, on the one hand, there was no particular text that I wanted to follow, while on the other hand I wanted my students to have a convenient reference for the material in the course. I hope these notes were instructive to some readers of the blog.
During the second half of the course I will follows Arveson’s book “A Short Course on Spectral Theory”, besides some applications and/or examples that I will want to occasionally throw in. So I will post my notes on much rarer occasions.