Timeline for Differentiability of characteristic functions and moments of the corresponding measure
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 13, 2020 at 22:11 | comment | added | user69642 | I think it was stated by Zygmund in this paper projecteuclid.org/euclid.aoms/1177730443 but without proof. For a proof, you should have a look at his fundamental work on trigonometric series. | |
| Jun 13, 2020 at 15:57 | vote | accept | trisct | ||
| Jun 13, 2020 at 15:56 | comment | added | trisct | Thanks. I saw the example. But it was provided without proof that it is differentiable. Did Zygmund prove it? Can you give a reference to the proof of differentiability? | |
| Jun 13, 2020 at 15:36 | comment | added | user69642 | To complement my post and to counter the down vote: in the same chapter there is an example due to Zygmund of a characteristic function with a continuous first derivative but for which the associated law has an infinite first moment... | |
| Jun 13, 2020 at 12:47 | history | answered | user69642 | CC BY-SA 4.0 |