Let me answer your two questions in reverse order:

b) The German word <A HREF="https://books.google.nl/books?id=vai7wiq5HIYC&pg=PA1695">Zackenfunktion</A> ("spiky function") refers to what known as a <A HREF="https://en.wikipedia.org/wiki/Dirac_delta_function">Dirac delta function.</A>  

a) The delta function has the property that $\int_{-\infty}^\infty \delta(y-x)f(x)\,dx=f(y)$, hence the identity used by Van Cittert.