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.
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页码：2759 / 2774
页数：16
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