Timeline for Quick proofs of hard theorems
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| May 30, 2010 at 14:59 | comment | added | Carl Offner | It's a great example, of course. The Banach algebra in question is $l^1$ with the algebra multiplication being convolution. I haven't looked at this in a while, but when I did look at Weiner's original work, it struck me that he was using convolution in a very modern way -- the whole argument was based on properties of convolution, and the algebraic properties in particular were key. I've occasionally wondered if Gelfand noticed this aspect and if it was in any way an inspiration for what he did. | |
| May 17, 2010 at 1:12 | comment | added | Jonas Meyer | For Wiener's proof, see Lemma IIe in "Tauberian theorems", 1932: jstor.org/stable/1968102. | |
| May 17, 2010 at 1:01 | comment | added | Jonas Meyer | Gelfand's result was first published in 1939 ("On normed rings" announces the basics of the new theory, "To the theory of normed rings II" has this application and more), although a 1941 paper ("Normierte Ringe") which provides more details and proofs seems to be more often cited. These are in the Collected papers, volume 1. | |
| May 16, 2010 at 19:11 | history | answered | Paul Siegel | CC BY-SA 2.5 |