APM346-2012 > Final Exam

problem 4

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Victor Ivrii:
I finished grading problem 4(a),(b). While (a) was mastered by many, only few managed with (b).

Also some tried to prove that $\lim_{t\to \infty} k(t)=\lim_{t\to \infty} p(t)=\frac{1}{2}E$ while in fact a stronger statement was required $p(t)=q(t)=\frac{1}{2}E$ for $|t|\ge T$.

The weaker statement could be proven then under relaxed condition $E<\infty$ instead of $f,g$ being supported in $|x|\le M$.

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