Timeline for Odd function on the 2-sphere whose integrals over all hemispheres is zero
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Nov 21, 2017 at 5:26 | vote | accept | Asaf Shachar | ||
| Nov 13, 2017 at 18:15 | comment | added | Igor Rivin | @fedja My claim is that the argument given here is reasonably self-contained, and does not require any knowledge of Funk transform (or its existence). It seems unlikely that one can get the result without the representation theory (though I would be happy to be proven wrong...) | |
| Nov 13, 2017 at 18:09 | comment | added | fedja | "Without relying on the invertibility of the Funk transform" seems to be the crucial part of the question. Of course, your convolution is not exactly that, but I would say that the invertibility of the Funk transform is easier (just because the roots of orthogonal polynomials interlace and all odd polynomials vanish at $0$, so no even one does). | |
| Nov 13, 2017 at 17:53 | history | answered | Igor Rivin | CC BY-SA 3.0 |