A fresh approach to the Paley-Wiener theorem for Mellin transforms and the Mellin-Hardy spaces

被引：11

作者：

Bardaro, Carlo ^{[1
]}

Butzer, Paul L. ^{[2
]}

Mantellini, Ilaria ^{[1
]}

Schmeisser, Gerhard ^{[3
]}

机构：

[1] Univ Perugia, Dept Math & Comp Sci, Via Vanvitelli 1, I-06123 Perugia, Italy

[2] Rhein Westfal TH Aachen, Lehrstuhl Math A, Templergraben 55, D-52056 Aachen, Germany

[3] FAU Erlangen Nurnberg, Dept Math, Cauerstr 11, D-91058 Erlangen, Germany

来源：

MATHEMATISCHE NACHRICHTEN | 2017年 / 290卷 / 17-18期

关键词：

Mellin transforms; Paley-Wiener spaces; Riemann surfaces; Paley-Wiener theorem; Mellin-Bernstein spaces; polar-analytic functions; DILATIONALLY INVARIANT TRANSFORMS; EXPONENTIAL-SAMPLING METHOD; LAPLACE;

D O I：

10.1002/mana.201700043

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Here we give a new approach to the Paley-Wiener theorem in a Mellin analysis setting which avoids the use of the Riemann surface of the logarithm and analytical branches and is based on new concepts of polar-analytic function in the Mellin setting and Mellin-Bernstein spaces. A notion of Hardy spaces in the Mellin setting is also given along with applications to exponential sampling formulas of optical physics.

引用

页码：2759 / 2774

页数：16

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