Aufgaben:Problem 13

In the first part of the solution for problem one, the derivative w.r.t time of \(\xi\) is never used... it either be changed to the actual usecase, or left away as it is shown in the next steps.

Also one may should show that \(\frac{d}{dt}\left(\int_0^t\phi\left( s\right)ds\right) = \phi\left( t\right)\)

Regards Patrick

Thank you for your hint. My previous attempt used this derivative, so you're absolutely right, I can certainly delete that. I think the second statement is actually a formulation of the Fundamental Theorem of Calculus, so I will put that as a remark behind the step where I used it.

Cheers Valentin

Ah and I'm sorry I put an extra in \( x \) to clarify that the function is \( 2\pi-\)periodic in \( x \). Did forget to mention it.

Regards Patrick

In the Solution of a) after we know that the derivative of xi is less than or equal to zero, i would just say that since xi is continues it is monotonically decreasing and thus \( \xi(t) \leq \xi(0) \), the claim follows. "Carl (talk) 22:06, 17 January 2015 (CET)"