# Remind me where to find a proof of a spectral theorem for RHS

1. Apr 23, 2014

### Fredrik

Staff Emeritus
I know I've seen a very short article (3-5 pages) with a proof of a spectral theorem for rigged Hilbert spaces, written for people who already know the usual spectral theorems, by some guy who I think had a muslim name. Anyone know what I'm talking about? It's been posted here before, almost certainly more than once, but I just spent 20 minutes trying to find it here and on my computer, so I think it's time to just ask.

No need to hurry to get me an answer right away. I'm not even going to read it right away. I'm just making a to-do list about things I'd like to understand better, and I want to put this article on the list.

(I think I may even have asked this question before, LOL).

2. Apr 23, 2014

### micromass

You can always try Gelfand-Vilenkin's Generalized functions, Volume 4. However, the proof there has a mistake, which is not easily solved (but can be solved).
My favorite book is "Methods of Hilbert spaces" by Maurin. It states the proof in a different form than Gelfand-Vilenkin, and a form that I think is more useful. Than again, he doesn't explicitely say anything about RHS (he obviously does use the concept though). Other than that, the book really covers a lot of nice things about Hilbert spaces. I don't understand why the book is not more popular.

3. Apr 23, 2014

### Fredrik

Staff Emeritus
Thanks micro. I'll make a note of those books before I forget them too. It's interesting to hear that you liked Maurin's book. One of the reasons why I haven't checked it out is that I found a negative review about it, that complained about the presentation, inconsistencies in notation, and even some incorrect statements. Link.

I still suspect that the short article I've seen is the best place to study the theorem and its proof. I just wish I could remember. I hope that Strangrep or dextercioby does.

4. Apr 23, 2014

### Fredrik

Staff Emeritus
I found the document I had in mind. It's a 5-page pdf document with the title "Generalized eigenfunctions" written by a guy named Mustafa Kesir. Some other guy named Christopher King has a copy on his web page: http://mathserver.neu.edu/~king_chris/GenEf.pdf.

5. Apr 23, 2014

### dextercioby

I remember saying sometimes in the past that Kesir almost copy-pasted in his work one of the appendices of Berezin & Shubin's 'SchrÃ¶dinger equation' which had been based on Berezanskii's work and book in the 1960's.

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