  H. Landau's necessary density conditions for sampling and interpolation may
be viewed as a general principle resting on a basic fact of Fourier analysis:
The complex exponentials $e^{i kx}$ ($k$ in $\mathbb{Z}$) constitute an
orthogonal basis for $L^2([-\pi,\pi])$. The present paper extends Landau's
conditions to the setting of locally compact abelian (LCA) groups, relying in
an analogous way on the basics of Fourier analysis. The technicalities--in
either case of an operator theoretic nature--are however quite different. We
will base our proofs on the comparison principle of J. Ramanathan and T.
Steger.
