Timeline for Determine if an integral expression is in $L^2(\mathbb{R})$
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 14, 2022 at 11:08 | vote | accept | Gateau au fromage | ||
| Aug 5, 2022 at 15:00 | comment | added | Christian Remling | @Gateauaufromage: Yes, this is what I had in mind. | |
| Aug 4, 2022 at 19:49 | comment | added | Gateau au fromage | @Christian Remling I looked at the books given in reference to that Wikipedia article and found the precise statements. Thank you very much for the information. I had never seen that result before. | |
| Aug 4, 2022 at 19:48 | answer | added | Gateau au fromage | timeline score: 2 | |
| Aug 4, 2022 at 19:16 | comment | added | Gateau au fromage | @Christian Remling Let me see if I get this straight. I am looking at the first inequality of the section entitled "Common usage and Young's inequality". If the two "sups" on its RHS are finite, then it gives me an upper bound on the operator bound AND it shows that the operator is well-defined in all of $L^2$ and is continuous. Is that right? | |
| Aug 4, 2022 at 19:11 | comment | added | Gateau au fromage | @WillieWong Yes, that's it. | |
| Aug 4, 2022 at 14:53 | comment | added | Christian Remling | You're considering the integral operator with kernel $K(x,y)=e^{x-y}\chi_{y>x}$. Schur's test shows that this is bounded $L^2\to L^2$: en.wikipedia.org/wiki/… | |
| Aug 4, 2022 at 12:22 | comment | added | Willie Wong | In this context, which space is $H^1$? The Sobolev space of functions such that $f, f'$ are both in $L^2$? | |
| Aug 4, 2022 at 11:04 | history | edited | Gateau au fromage | CC BY-SA 4.0 |
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| Aug 4, 2022 at 10:53 | history | asked | Gateau au fromage | CC BY-SA 4.0 |