Various kinds of sensitive singular perturbations

Nicolas Meunier; Jacqueline Sanchez-Hubert; Évariste Sanchez-Palencia

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Between the Paley-Wiener theorem and the Bochner tube theorem

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We present the classical Paley-Wiener-Schwartz theorem [1] on the Laplace transform of a compactly supported distribution in a new framework which arises naturally in the study of the Mellin transformation. In particular, sufficient conditions for a function to be the Mellin (Laplace) transform of a compactly supported distribution are given in the form resembling the Bochner tube theorem [2].