harmonic analysis?

Current License: CC BY-SA 3.0

35 events

when toggle format	what		by	license	comment
Mar 12, 2023 at 18:27	answer	added	B K		timeline score: 2
Jun 11, 2020 at 8:04	comment	added	Qi Zhu		I haven't read it but it might be worthwhile to mention the book "Lectures and Exercises on Functional Analysis" by A. Ya. Helemskii who starts his book by introducing 50 pages of basic category theory.
Apr 13, 2017 at 12:19	history	edited	CommunityBot		replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
Nov 17, 2012 at 17:24	answer	added	jbc		timeline score: 10
Oct 2, 2012 at 9:27	answer	added	Peter Michor		timeline score: 8
Dec 29, 2011 at 1:51	answer	added	Benjamin Steinberg		timeline score: 7
Dec 28, 2011 at 1:09	answer	added	Iian Smythe		timeline score: 6
Dec 22, 2011 at 8:01	answer	added	Mark Kim-Mulgrew		timeline score: 11
Dec 16, 2011 at 13:38	answer	added	Mkouboi		timeline score: 5
Dec 16, 2011 at 10:14	history	edited	Yemon Choi	CC BY-SA 3.0	changed title because it was bugging me, man
Dec 15, 2011 at 4:27	comment	added	Yemon Choi		I guess my main problem with the question as it stands is this: functional analysis studies objects, and these objects often fit together into a sensible category ... so of course category theory can be used in the development or practice of analysis. I would be happier with a question that asks "do analysts find category theory helps them do X?" than "can you find category theory when considering analysis-ish things?"
Dec 15, 2011 at 2:19	comment	added	Eric		@Yemon: My comment has been transferred to an answer. Questions like this concerning category theory are always tricky to ask as well as answer. I think the power of category theory comes from its usefulness as an organizational tool, and that it gives an easier, more structured way to look at the big picture. I feel like the best way to see the usefulness of category theory in these terms is by just seeing a lot of examples.
Dec 15, 2011 at 2:08	answer	added	Eric		timeline score: 9
Dec 15, 2011 at 0:46	comment	added	Yemon Choi		@Eric: if you think it's worth mentioning, add it as an answer. It is not clear to me that it answers the original question, but then it's not clear to me what the original question actually wants.
Dec 15, 2011 at 0:38	comment	added	Eric		This is a pretty well-known example, but I like too much to go without mentioning it. The Gelfand representation gives an equivalence between the category of commutative, unital C*-algebras and the opposite category of compact Hausdorff spaces.
Dec 15, 2011 at 0:14	answer	added	Rogier Brussee		timeline score: 37
Dec 14, 2011 at 12:24	answer	added	Ronnie Brown		timeline score: 17
Dec 14, 2011 at 12:03	answer	added	Martin Brandenburg		timeline score: 20
Dec 14, 2011 at 6:28	answer	added	Denis Serre		timeline score: 4
Dec 14, 2011 at 0:31	answer	added	paul garrett		timeline score: 84
Dec 14, 2011 at 0:23	comment	added	Yemon Choi		@Dan: could you perhaps reword your question to make it clearer what kind of "uses" you have in mind. Your question suggests that you are looking for applications in analysis, but then your comment says you are looking for things which give analysis a category-theoretic foundation. If you make the question more precise then people may be able to give more focused/relevant answers
Dec 14, 2011 at 0:21	comment	added	KConrad		At least the basic language of category theory is useful in putting the initial theorems about analysis on locally compact abelian groups into a clean framework (to bring out the analogies with finite-dimensional vector spaces over a field).
Dec 13, 2011 at 22:56	comment	added	Michael Greinecker		His view on measure theory seems to be that one shouldn't work with measure spaces but with measure algebras, the boolean algebras one gets from a measure space when quotienting out by the ideal of null sets. The resulting structure is still very "analytic" and Fremlin devotes all of volume V of his grand epos on measure theory to them.
Dec 13, 2011 at 22:49	comment	added	Yemon Choi		@Michael: Isn't Dmitri's perspective more like "things traditionally seen as the province of Analysis should really be seen/defined/formulated using category theory"? Which I view as slightly different from the question here, though I may have misunderstood
Dec 13, 2011 at 22:27	answer	added	Paul Siegel		timeline score: 28
Dec 13, 2011 at 22:01	comment	added	Michael Greinecker		I think Dmitri Pavlov has a lot to say on this topic, see for eaxample <a href="mathoverflow.net/questions/20740/…>
Dec 13, 2011 at 21:21	answer	added	Finn Lawler		timeline score: 14
Dec 13, 2011 at 20:55	answer	added	Peter Arndt		timeline score: 2
Dec 13, 2011 at 20:04	history	edited	Benjamin Steinberg	CC BY-SA 3.0	deleted 42 characters in body; edited tags; edited tags
Dec 13, 2011 at 19:52	comment	added	Dan		@Yemon Choi I was more looking for books that try to put a foundation on Mathematical Analysis via Category theory sort of like the Mathematics made difficult book where he tries to put elementary Maths in terms of Category theory.
Dec 13, 2011 at 19:46	history	edited	Dan	CC BY-SA 3.0	added 108 characters in body; Post Made Community Wiki
Dec 13, 2011 at 19:44	comment	added	Yemon Choi		Also, please add a link to the cross-post (just so that people here don't unwittingly duplicate what has been said there). Thanks
Dec 13, 2011 at 19:42	comment	added	Yemon Choi		Personally, I think this question is a bit vague - functional analysis is by now a very broad church - but in any case you should make this question "Community Wiki" by clicking the appropriate box. This is the preferred option for questions which seek a big list of rankable items, rather than a single "right" or definitive answer
Dec 13, 2011 at 19:38	history	edited	Dan	CC BY-SA 3.0	edited body
Dec 13, 2011 at 19:19	history	asked	Dan	CC BY-SA 3.0

toggle format