  We derive spectral width estimates for traces of tempered solutions of a
large class of multiplier equations in $\mathbf{R}^n$. The estimates are
uniform for solutions up to a given order. In the process, we find a rather
explicit expression for a tempered fundamental solution of a multiplier. We
successfully verify our spectral width estimates against numerical results in
several scenarios involving the inhomogeneous Helmholtz equation in
$\mathbf{R}^n$ with $n=1,\dots,9$. Our main result is directly applicable in
the stability analysis of solutions of inverse source problems.
