existence of Laplace transform

Theorem 1.

For every measurable functionMathworldPlanetmath f:[0,)C, if there exists a real number t0 such that


converges, then the Laplace transformMathworldPlanetmath L(f) is a well-defined function from {tCt>t0} to C. Furthermore, the Laplace transform function is analytic.

Title existence of Laplace transform
Canonical name ExistenceOfLaplaceTransform
Date of creation 2013-03-22 16:31:12
Last modified on 2013-03-22 16:31:12
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 7
Author rspuzio (6075)
Entry type Theorem
Classification msc 42-01