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Otto Liess, Yasunori Okada & Nobuyuki Tose

Second Hyperfunctions, Regular Sequences, and Fourier Inverse Transforms

(Volume 70 - Année 2001 — Numéro 4 - 5 - 6)
Open Access
Mots-clés : second hyperfunctions, microfunctions with holomorphic parameters, Fourier transform


Second hyperfunctions are formal boundary values of microfunctions with holomorphic parameters defined on wedges in much the same way in which classical hyperfunctions are boundary values of holomorphic functions defined on wedges. Since microfunctions with holomorphic parameters are themselves already defined in a formal way, second hyperfunctions have a rather non-intuitive definition and few explicit examples of second hyperfunctions which are not classical are known. In this paper we shall show that one can arrive at a better understanding by introducing the notion of regular sequences of holomorphic functions. We shall then show that representation of second hyperfunctions in terms of regular sequences is quite efficient in the context of regularization of the Fourier-inverse transform of functions which appear in second microlocalization.

To cite this article

Otto Liess, Yasunori Okada & Nobuyuki Tose, «Second Hyperfunctions, Regular Sequences, and Fourier Inverse Transforms», Bulletin de la Société Royale des Sciences de Liège [En ligne], Volume 70 - Année 2001, Numéro 4 - 5 - 6, 307 - 343 URL :

About: Otto Liess

Universita di Bologna, Dipartimento di Matematica, Piazza Porta S. Donato 5, 40127 Bologna, Italy,

About: Yasunori Okada

Chiba University, Department of Mathematics, Yayoi 1-33, Inage-ku, Chiba 263-8522, Japan,

About: Nobuyuki Tose

Keio University, Hiyoshi Campus, Hiyoshi 4-1-1, Kohoku, Yokohama 223-8521, Japan,