TMA4230 Functional analysis 2005

Syllabus («pensumliste»)

In other words, what you are supposed to have read:

Erwin Kreyszig: Introductory functional analysis with applications. Chapters 4, 7, 9.

My own notes: Assorted notes on functional analysis. Chapters 2–7.

Note that there is a great deal of overlap between Kreyszig's book and my notes. Obviously, in those cases I think my notes are better (or else I would not have written them), but you're free to read one or the other, or both, where there is overlap.

Exceptions: The following material is not included, or is only partially included where indicated:

• Kreyszig 4.4: No detailed knowledge required.
• Kreyszig 4.10: Not included.
• Kreyszig 4.11: No detailed knowledge required.
• Kreyszig 7.2: I haven't bothered to introduce point spectrum, continuous spectrum, and residual spectrum. So you don't need to remember those definitions.
• Kreyszig 7.4-2: I don't know what he was thinking of when he wrote that proof. Read it at your own peril, if you must.
• My notes, chapter 4 (topology): No direct questions will be asked, but you will need a basic understandig of some toplogical concepts.
• My notes, chapter 7 (compact operators and Hilbert–Schmidt operators): No detailed knowledge required. But you should learn the definition of compact operator and the statement of the spectral theorem for compact self-adjoint operators.

General: There is no point in trying to learn all the proofs or anything like that. What I am hoping is that you will know all the big theorems and several smaller ones, and have a working understanding of how they can be used. I shall try to make exam problems that don't require great ingenuity on your part (possibly with a single exception), but rather problems that require a simple, straightforward application of the theory. (Yes, I know that perceptions of what straightforward means differ.) Other problems will simply require you to state known facts. Be sure you learn the precise conditions for applying each of the big theorems.

Harald Hanche-Olsen Oppdatert: 2005–05–19 15:33