### Abstract

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 language | English |
---|---|

Pages (from-to) | 307-343 |

Number of pages | 37 |

Journal | Bulletin de la Societe Royale des Sciences de Liege |

Volume | 70 |

Issue number | 4-6 |

Publication status | Published - 2001 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Environmental Engineering

### Cite this

*Bulletin de la Societe Royale des Sciences de Liege*,

*70*(4-6), 307-343.

**Second hyperfunctions, regular sequences, and Fourier inverse transforms.** / Liess, Otto; Okada, Yasunori; Tose, Nobuyuki.

Research output: Contribution to journal › Article

*Bulletin de la Societe Royale des Sciences de Liege*, vol. 70, no. 4-6, pp. 307-343.

}

TY - JOUR

T1 - Second hyperfunctions, regular sequences, and Fourier inverse transforms

AU - Liess, Otto

AU - Okada, Yasunori

AU - Tose, Nobuyuki

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

KW - Fourier-transform

KW - Microfunctions with holomorphic parameters

KW - Second hyperfunctions

UR - http://www.scopus.com/inward/record.url?scp=0035738658&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035738658&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0035738658

VL - 70

SP - 307

EP - 343

JO - Bulletin de la Societe Royale des Sciences de Liege

JF - Bulletin de la Societe Royale des Sciences de Liege

SN - 0037-9565

IS - 4-6

ER -