Timeline for Riesz transform of constant function
Current License: CC BY-SA 4.0
4 events
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| Sep 14 at 18:46 | comment | converted from answer | Andrew_UELtd | I don't think the definition is right. I think it should be p.v.\int_R dx p.v.\int_R dy (integrand), which is how a Hilbert transform in 2D is defined. A multi-dimensional Hilbert transform of dimension n is NOT zero when n is even, only when it is odd. When n is even the Hilbert transform of a constant k is equal to (-1)^{n/2} k, which follows as a corollary to result equation 22.181 of King "Hilbert Transforms, vol 2." I don't know if this helps with your question, but it looks to be related. | |
| Apr 8, 2022 at 3:52 | history | edited | Fozz | CC BY-SA 4.0 |
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| Apr 8, 2022 at 3:45 | history | edited | Fozz | CC BY-SA 4.0 |
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| Apr 8, 2022 at 3:37 | history | asked | Fozz | CC BY-SA 4.0 |