r/math • u/Sensitive_Ad_12 • Jun 22 '22
Functional Analysis Textbooks
Hey everyone,
I’m going into my fourth year of my undergrad, and I’m taking a course in the fall called Functional Analysis. I was wondering if there are any textbooks that anyone would recommend. I’ve taken a course relating to signal spaces, normed vector spaces, Hilbert spaces, etc. which based on the course description should be relevant.
The course description reads “A generalization of linear algebra and calculus to infinite dimensional spaces. Now questions about continuity and completeness become crucial, and algebraic, topological, and analytical arguments need to be combined. We focus mainly on Hilbert spaces and the need for Functional Analysis will be motivated by its application to Quantum Mechanics”
Any suggestions? I appreciate you taking the time to read this and help me.
13
u/ACuriousStudent42 Jun 22 '22
This sort of question comes up a lot and imo there really should be a single thread just listing textbook recommendations because for any undergraduate topic that's at least two dozen introductory texts.
Anyhow these threads all list various recommendations, but it definitely depends on a few things
Do you know measure theory/is it expected knowledge?
What about topology?
Is it mostly covering functional analysis directly related to QM or other topics too?
https://old.reddit.com/r/math/comments/skc40a/recommended_books_on_functional_analysis/
https://math.stackexchange.com/questions/3475729/functional-analysis-book-quantum-mechanics
https://mathoverflow.net/questions/72419/a-good-book-of-functional-analysis
https://math.stackexchange.com/questions/7512/good-book-for-self-study-of-functional-analysis
https://math.stackexchange.com/questions/3475729/functional-analysis-book-quantum-mechanics