Timeline for Functional derivative of the square of an integral

8 events

when toggle format	what		by	license	comment
Aug 8, 2012 at 17:26	comment	added	Liviu Nicolaescu		Try to use the ideas in Update 2.
Aug 8, 2012 at 16:07	history	edited	Liviu Nicolaescu	CC BY-SA 3.0	added 877 characters in body
Aug 8, 2012 at 14:14	comment	added	Pierre Robert		Thanks, Do you foresee any possibilities to actually solve the system? I tried it out, but get stuck pretty fast....
Aug 8, 2012 at 13:26	vote	accept	Pierre Robert
Aug 7, 2012 at 22:29	history	edited	Liviu Nicolaescu	CC BY-SA 3.0	added 11 characters in body
Aug 7, 2012 at 22:21	history	edited	Liviu Nicolaescu	CC BY-SA 3.0	added 1023 characters in body; added 2 characters in body
Aug 7, 2012 at 18:56	comment	added	Pierre Robert		Thanks. This was only a part of a bigger thing. Would you mind also taking a look at the following? $I(G(\omega)) = \int_{-\kappa\pi}^{\kappa\pi} \frac{A}{G(\omega)+A}d\omega-\frac{\| \int_{-\kappa\pi}^{\kappa\pi} \frac{A}{G(\omega)+A}\exp(-i\omega)d\omega\|^2}{ \int_{-\kappa\pi}^{\kappa\pi} \frac{A}{G(\omega)+A}d\omega}$, where $\kappa<1$, $A>0$, and $G(\omega)\geq 0$. Now I would like to minimize $I(G(\omega))$ under the constraint of unit area of $G(\omega)$, i.e., $\int_{-\kappa \pi}^{\kappa \pi} G(\omega)d\omega=1$. My hypothesis is that a flat $G(\omega)=1/2\kappa\pi$ is optimal.
Aug 7, 2012 at 15:06	history	answered	Liviu Nicolaescu	CC BY-SA 3.0