Timeline for Proving that a space is Hilbert
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| May 4, 2015 at 15:02 | answer | added | Robert | timeline score: 1 | |
| Nov 25, 2014 at 18:18 | comment | added | Robert | If we take the Fourier transform, we get $$\|(l^2-x^2)\hat\phi\|_{L^2}\leq K_1\Big(\|\hat{f}\|_{L^2}+\|\hat{h}\|_{L^2}+\|\hat{g}\|_{L^2}\Big).$$ So, If $l>\ell$ then $\|\hat{\phi}\|_{L^2}\leq K_2\|(l^2-x^2)\hat\phi\|_{L^2}$ with $K_2>0$ and thus (by Plancherel theorem), $\|\phi\|_{L^2}\leq K_3\|(\phi,\psi,w)\|_1$. Working in a similar way with the others functions, we get the desired result. Is this the solution that you suggested? Did you assume $l> \ell$ or am I missing something? | |
| Nov 22, 2014 at 1:37 | comment | added | Michael Renardy | Consider how you would go about solving the problem $$\phi_x+\psi+lw=f,$$ $$w_x-l\phi=g,$$ $$\psi_x=h,$$ with $f,g,h\in L^2$. The inequality you need will come as a byproduct. | |
| Nov 21, 2014 at 23:20 | history | edited | Robert | CC BY-SA 3.0 |
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| Nov 20, 2014 at 13:14 | history | edited | Robert | CC BY-SA 3.0 |
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| Nov 20, 2014 at 12:19 | history | edited | Robert | CC BY-SA 3.0 |
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| Nov 20, 2014 at 7:48 | review | First posts | |||
| Nov 20, 2014 at 7:49 | |||||
| Nov 20, 2014 at 7:46 | history | asked | Robert | CC BY-SA 3.0 |