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The Laplace Transforms of Several Special Distributions

  • Gustav Doetsch

Abstract

$$ \underline {T = \delta } $$
(1.)
The distribution δ is of finite order for it is equal to D2 h(t) where h(t) designates the continuous unit ramp function defined by (12.1), which satisfies both conditions (12.4,5), the second condition with σ = 0. Hence δ has a ℒ-transform, which is given by
$${\cal L}\left\{ \delta \right\}\, = \,{s^2}{\cal L}\left\{ {h\left( t \right)} \right\}\, = \,{s^2}{\cal L}\left\{ t \right\}\, = \,{s^2}\frac{1}{{{s^2}}}\, = \,1\,\,\,{\rm{for}}\,\Re s > 0$$
(1)
.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • Gustav Doetsch
    • 1
  1. 1.Emeritus of MathematicsUniversity of FreiburgFreiburg i. Br.Germany

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