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1996•Journal of International Crisis and Risk Communication ResearchOpen access

A comparison of the two-sided laplace transform and the mellin transform

Glorida L. Porter

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Abstract

Abstract : The reals with addition and the positive reals with multiplication are isomorphic as groups. From that point of view, the two-sided Laplace transform and the Mellin transform are different representations of the same transform. This allows us to easily derive the properties of the Mellin transform from the properties of the two-sided Laplace transform. The method extends to functions of several variables as well.

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What this paper is about

Abstract : The reals with addition and the positive reals with multiplication are isomorphic as groups. From that point of view, the two-sided Laplace transform and the Mellin transform are different representations of the same transform. This allows us to easily derive the properties of the Mellin transform from the properties of the two-sided Laplace transform. The method extends to functions of several variables as well.

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Available abstract

Abstract : The reals with addition and the positive reals with multiplication are isomorphic as groups. From that point of view, the two-sided Laplace transform and the Mellin transform are different representations of the same transform. This allows us to easily derive the properties of the Mellin transform from the properties of the two-sided Laplace transform. The method extends to functions of several variables as well.

Key concepts: Mellin transform, Two-sided Laplace transform, Mellin inversion theorem, Laplace transform, Inverse Laplace transform, Laplace transform applied to differential equations, Mathematics, Laplace–Stieltjes transform

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