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

共 32 条

[1] On real Paley-Wiener theorems for certain integral transforms [J].

Andersen, NB .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 288 (01) :124-135

[2] REAL PALEY-WIENER THEOREMS AND LOCAL SPECTRAL RADIUS FORMULAS [J].

Andersen, Nils Byrial ;

de Jeu, Marcel .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 362 (07) :3613-3640

[3]

[Anonymous], 1986, REAL COMPLEX ANAL

[4]

[Anonymous], 1982, Mathematical Notes, DOI DOI 10.1515/9780691222455

[5] Mellin analysis and its basic associated metric-applications to sampling theory [J].

Bardaro, C. ;

Butzer, P. L. ;

Mantellini, I. ;

Schmeisser, G. .

ANALYSIS MATHEMATICA, 2016, 42 (04) :297-321

[6]

Bardaro C., 2014, Sampl. Theory Signal Image Process, V13, P35, DOI [10.1007/BF03549572, DOI 10.1007/BF03549572]

[7] On the Paley-Wiener theorem in the Mellin transform setting [J].

Bardaro, Carlo ;

Butzer, Paul L. ;

Mantellini, Ilaria ;

Schmeisser, Gerhard .

JOURNAL OF APPROXIMATION THEORY, 2016, 207 :60-75

[8] The Mellin-Parseval formula and its interconnections with the exponential sampling theorem of optical physics [J].

Bardaro, Carlo ;

Butzer, Paul L. ;

Mantellini, Ilaria .

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2016, 27 (01) :17-29

[9] EXPONENTIAL-SAMPLING METHOD FOR LAPLACE AND OTHER DILATIONALLY INVARIANT TRANSFORMS .2. EXAMPLES IN PHOTON-CORRELATION SPECTROSCOPY AND FRAUNHOFER-DIFFRACTION [J].

BERTERO, M ;

PIKE, ER .

INVERSE PROBLEMS, 1991, 7 (01) :21-41

[10] EXPONENTIAL-SAMPLING METHOD FOR LAPLACE AND OTHER DILATIONALLY INVARIANT TRANSFORMS .1. SINGULAR-SYSTEM ANALYSIS [J].

BERTERO, M ;

PIKE, ER .

INVERSE PROBLEMS, 1991, 7 (01) :1-20

← 1 2 3 4 →