harmonic analysis?

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Jul 13, 2020 at 10:39	comment	added	Tom Copeland		Nice answer. (How did I know this was written by Paul Garrett before I checked the revision attribution?) Anyway, ambiguity tolerance is needed to accomodate different styles of learning. One proceeds from the concrete to the abstract, and another, from the abstract to the concrete--both approaches quite rational with the former dominating the evolution of theory, e.g., the derivative from notions of motion and tangency rather than the algebraic formulation of a derivation on a product of whatever. You weren't born with fully functional vision. Took interaction with the environment/ objects.
Dec 15, 2011 at 0:47	comment	added	Yemon Choi		-1 for penultimate paragraph in latest edit ;)
Dec 14, 2011 at 9:38	comment	added	Yemon Choi		@Paul: I have time, and liking for, both styles of analysis myself. Each has its merits and each can have its place
Dec 14, 2011 at 9:33	comment	added	Yemon Choi		@pm Not in the category of Banach spaces and linear contractions it isn't... the dual of a coproduct is the product of the duals
Dec 14, 2011 at 8:28	comment	added	Marc Palm		I find it particularly helpful about the limits of vector spaces, that the dual of a limit is the colimit of the duals....
Dec 14, 2011 at 2:11	history	edited	paul garrett	CC BY-SA 3.0	added 1982 characters in body
Dec 14, 2011 at 0:44	comment	added	Yemon Choi		Oh, and +1 (this is more or less my own use of category theory)
Dec 14, 2011 at 0:37	comment	added	Yemon Choi		Helemskii has a book "Lectures on Functional Analysis" (or some similar title) where he covers some of the results one would normally associate with Rudin Chapters 1 to 4, but with forgeful functors and the such-like. Unfortunately I haven't got access to a copy to check.
Dec 14, 2011 at 0:35	comment	added	Yemon Choi		Which functional analysts are these, then, who don't like to speak of Frechet spaces as (projective/inverse) limits of Banach spaces in an appropiate category of TVSes?
Dec 14, 2011 at 0:31	history	answered	paul garrett	CC BY-SA 3.0