Spectral Measure and Resolution of Identities.

Question

I am currently reading topics related to Spectral Measure and Resolution of Identities. I am new to this area and reading it from Rudin's Book on Functional Analysis.

Can someone refer to some other books or lecture notes, where I can find this topic explained for self study.

Thank You.

Answer 1

1. "Unbounded Self-adjoint Operators on Hilbert Space" by Konrad Schmüdgen.

Is a modern introduction to unbounded operators. You can read the chapter about spectral measures and integrals of bounded functions, or unbounded functions if you need it for unbounded operators.

2. "Functional Analysis", vol I,II, by Berezanskii, Sheftel, Us.

Is a very detailed introduction to functional analysis and operator theory.

3. Akhiezer, Glazman "Theory of Linear Operators in Hilbert Space".

Is a well-written classical book.

These books contain a lot of exercises, which help to understand the topic.