3
$\begingroup$

(This is a literature/reference question.)

So... long story short:

(1) In my present research, I needed a theory of continuous functions from the $p$-adic integers to the $q$-adic integers. Unable to find a quick answer online, I ended up writing a paper (un-published) in which I worked out the basic details of this theory, developed an integration theory, translation-invariant measures, a Fourier transform, and so on.

(2) Just recently, after traveling down the rabbit hole of the literature, I've found that much (if not all) of what I did in my paper—along with quite a bit of extra details—were covered in A.C.M Rooij's Non-Archimedean Functional Analysis (1978). Unfortunately, this book is now woefully out-of-print; cheapest available copy I could find is $250 (US).

(3) I was fortunate enough to be able to at least find a copy of the table of contents of Rooij's book; scroll down to the bottom of the linked page to see it. Chapters 5 through 9 are what I need.

My question: What are some non-out-of-print books that cover this material? (Preferably with as little abstract nonsense as possible)

I ask because the books I immediately pull up when searching for "non-archimedean functional analysis" end up being riddled with either rigid analytic spaces and/or modern abstract nonsense, as opposed to the clean and direct analysis that I'm looking & hoping for. Any help would be much appreciated.

$\endgroup$
6
  • 5
    $\begingroup$ The book can be found online, through certain repositories which collect copies of books online. I believe the site policy disallows me from sharing a link directly, but it shouldn't be hard to find if you search for how to access scientific literature for free. $\endgroup$
    – Wojowu
    Commented Jun 13, 2020 at 21:27
  • 3
    $\begingroup$ since it's out of print, it's probably fair use to download it for personal use. $\endgroup$ Commented Jun 13, 2020 at 21:31
  • $\begingroup$ I've searched, but haven't been able to find more than the front matter, and Chapters 1 & 3. $\endgroup$
    – MCS
    Commented Jun 13, 2020 at 23:01
  • 4
    $\begingroup$ libgen.is $\endgroup$
    – efs
    Commented Jun 14, 2020 at 0:23
  • 2
    $\begingroup$ This books exists in university libraries (I first saw it in such places when I was a student). If you have an academic affiliation, you could request the book by interlibrary loan. Perhaps current events may slow down the process of getting it that way, but being out of print does not mean the book is genuinely inaccessible if you have borrowing privileges at a university library. $\endgroup$
    – KConrad
    Commented Jun 14, 2020 at 2:24

0

You must log in to answer this question.