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May 9, 2018 at 19:57 comment added robert bristow-johnson well, i up arrowed you @MattL. but this "new" definition of the Hilbert transform is one that, to be honest, that i had never heard of before. $$ $$ i never claimed to know everything.
May 9, 2018 at 11:42 comment added Matt L. I did the math and it all works out! (with the regularized version of the Hilbert transform for bounded functions). Please check the second part of my answer.
May 8, 2018 at 20:52 comment added robert bristow-johnson it's what the math.se guy said and pointed to exactly the same place you point to. my feeling is to stay-the-hell-away from some of these functions that don't converge.
May 8, 2018 at 20:18 comment added Matt L. I think the solution lies in the regularized Hilbert transform for $L^{\infty}$ functions.
May 8, 2018 at 18:46 history edited robert bristow-johnson CC BY-SA 4.0
added 19 characters in body
May 8, 2018 at 5:51 history answered robert bristow-johnson CC BY-SA 4.0