Second hyperfunctions, regular sequences, and Fourier inverse transforms

Otto Liess, Yasunori Okada, Nobuyuki Tose

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)307-343
Number of pages37
JournalBulletin de la Societe Royale des Sciences de Liege
Issue number4-6
Publication statusPublished - 2001 Dec 1


  • Fourier-transform
  • Microfunctions with holomorphic parameters
  • Second hyperfunctions

ASJC Scopus subject areas

  • General


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