[help] A laplace transform definition problem

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The discussion centers on the differences between two definitions of the Laplace transform, specifically regarding their treatment of distributions and measures. The first definition incorporates distributions such as the Dirac delta function and its derivatives, which have support at the origin. In contrast, the second definition excludes these distributions, leading to distinct interpretations in applications. Understanding these differences is crucial for proper application in mathematical and engineering contexts.

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goodness52200
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Hello all ^^

What is the difference between the two definitions

thanks a lot
 
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In a heuristic contest, the first one takes account of distributions/measures (for istance "Dirac delta function" and its derivatives) with support in the origin. The second one doesn't.
 

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