Let me answer your two questions in reverse order:
b) The German word Zackenfunktion ("spiky function") refers to the Dirac delta function, more commonly denoted with a lower case $\delta$.
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.