delay theorem

Theorem.  If  f(t)0  for  t<0  and  {f(t)}:=F(s),  one has


Proof.  Since  f(t-t0)0  for  t<t0,  the definition of Laplace transformMathworldPlanetmath at first gives


The substitution (  t-t0:=u  yields


Corollary.  For any f(t) and the Heaviside step function H(t), one has

Title delay theorem
Canonical name DelayTheorem
Date of creation 2013-03-22 18:02:46
Last modified on 2013-03-22 18:02:46
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 10
Author pahio (2872)
Entry type Theorem
Classification msc 44A10
Synonym delay theorem of Laplace transform
Related topic HeavisideStepFunction
Related topic TelegraphEquation