Timeline for Characterizing a functional that takes convolution to addition
Current License: CC BY-SA 3.0
9 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Oct 18, 2013 at 4:06 | comment | added | Henrique de Oliveira | @oferzeitouni Thanks! That seems to be very much in line with what I'm looking for. | |
| Oct 17, 2013 at 12:58 | comment | added | Steve Huntsman | en.wikipedia.org/wiki/Cauchy's_functional_equation | |
| Oct 17, 2013 at 3:21 | comment | added | ofer zeitouni | Alesker, Artstein, Faifman and Milman studied closely related questions in projecteuclid.org/… (see in particular their theorem 4). This applies to your map after exponentiation; they note that the real version of their result is in S. Alesker, S. Artstein-Avidan and V. Milman, A characterization of the Fourier transform and related topics, Linear and complex analysis, Amer. Math. Soc. Transl. Ser. 2, vol. 226, Amer. Math. Soc., Providence, RI, 2009, pp. 11–26. | |
| Oct 16, 2013 at 22:15 | comment | added | Henrique de Oliveira | @CarloBeenakker The Fourier transform has an image on complex-valued functions, so I believe the two are somewhat different. Besides, regarding the previous question, I'm still not sure if the Fourier transform is uniquely defined by that property. | |
| Oct 16, 2013 at 22:15 | comment | added | Henrique de Oliveira | @LoïcTeyssier I struggled a bit trying to decide what assumptions to add, but since the question asks for a characterization, what extra assumptions are needed---if any---is part of the question. I hope this doesn't make the question too vague; I would accept an answer that assumes linearity. Do you think I should reword the question? | |
| Oct 16, 2013 at 20:41 | comment | added | Carlo Beenakker | referring to this earlier related question you mention, isn't $H(f)$ just the logarithm of the (generalized) Fourier transform of $f$? | |
| Oct 16, 2013 at 19:10 | comment | added | Loïc Teyssier | I gather here that by "functional" you don't mean "linear", right? Do you imply on the other hand a continuity assumption? | |
| Oct 16, 2013 at 18:28 | history | asked | Henrique de Oliveira | CC BY-SA 3.0 |