Timeline for Examining the Hilbert transform of functions over the positive real line
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 20 at 12:50 | answer | added | an_ordinary_mathematician | timeline score: 2 | |
| Mar 14 at 21:41 | comment | added | Gabriel Palau | @ChristianRemling the no is for the first question I underestand. Any idea for the rest? | |
| Mar 14 at 21:40 | history | edited | Gabriel Palau | CC BY-SA 4.0 |
edited body
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| Mar 14 at 21:35 | history | edited | YCor | CC BY-SA 4.0 |
formatting
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| Mar 14 at 21:25 | comment | added | Gabriel Palau | thanks to both for the comments | |
| Mar 14 at 21:21 | comment | added | Christian Remling | No. $\{ f: \textrm{supp }f\subseteq [0,\infty) \}$ is a proper closed subspace of $L^2$ and $H$ is unitary. | |
| Mar 14 at 21:21 | comment | added | Aleksei Kulikov | For the first question of course not. If $Hf$ is close to $g$, then (since $H$ is continuous) $f = (-H)Hf$ is close to $-Hg$, so we can approximate $g$ (and indeed be equal to it) if and only if $-Hg$ is $0$ on $\mathbb{R}_{-}$. | |
| Mar 14 at 21:09 | history | edited | Gabriel Palau | CC BY-SA 4.0 |
edited title
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| Mar 14 at 20:59 | history | asked | Gabriel Palau | CC BY-SA 4.0 |