The Mellin Transform

Hélène Barucq 1, 2 Vanessa Mattesi 2, 1 Sébastien Tordeux 1, 2
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : The Mellin transform is an efficient tool to determine the behavior of a function at the neighbourhood of a point, in particular when the function admits a series expansion. This report aims at collecting some results related to this transform which turn out to be very useful when dealing with the behavior of the solution to the acoustic wave equation. We first recall the definition and some basic properties of the Mellin transform. Next, we explicit the relation between the behavior of a function in the the neighbourhood of the origin and the domain of analyticity of its Mellin transform.
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Hélène Barucq, Vanessa Mattesi, Sébastien Tordeux. The Mellin Transform. [Research Report] RR-8743, INRIA Bordeaux; INRIA. 2015, pp.16. ⟨hal-01165453v2⟩

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