Strip of convergence of the bilateral transform

Summary

The strip of convergence of a two-sided Laplace transform is the vertical strip $\alpha < \operatorname{Re} s < \beta$ in the complex plane where the defining integral converges absolutely. The left edge $\alpha$ is set by the growth of $f$ as $t \to +\infty$, and the right edge $\beta$ by its growth as $t \to -\infty$. Inside the strip the transform is holomorphic. The strip must be given along with the formula, since one formula can be the transform of different functions on different strips.