  We prove $L^{2}$ estimates and solvability for a variety of simply
characteristic constant coefficient partial differential equations $P(D)u=f$.
These estimates \[||u||_{L^2(D_{r})}\le C\sqrt{d_{r}d_{s}}
||f||_{_{L^2(D_{s})}}\] depend on geometric quantities - the diameters $d_{r}$
and $d_{s}$ of the regions $D_{r}$, where we estimate $u$, and $D_{s}$, the
support of $f$ - rather than weights. As these geometric quantities transform
simply under translations, rotations, and dilations, the corresponding
estimates share the same properties. In particular, this implies that they
transform appropriately under change of units, and therefore are physically
meaningful. The explicit dependence on the diameters implies the correct global
growth estimates. The weighted $L^{2}$ estimates first proved by Agmon in order
to construct the generalized eigenfunctions for Laplacian plus potential in
$\mathbb{R}^{n}$, and the more general and precise Besov type estimates of
Agmon and H\"ormander, are all simple direct corollaries of the estimate above.
