Stability Proof, continued

The same argument can be extended to the entire right-half plane as follows. Going back to

$$\frac{\sin(\nu)}{\nu} = e^\tau,$$

since $\left\vert\sin(\nu)/\nu\right\vert\leq 1$ for all real $\nu$ , and since $\left\vert e^\tau\right\vert>1$ for $\tau>0$ , this equation clearly has no solutions in the right-half plane. Therefore,

$$\zbox{\hbox{Any right-half-plane poles occur at $s=0$.}}$$