On the Paley-Wiener theorem in the Mellin transform setting

被引：21

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] PAU Erlangen Nurnberg, Dept Math, Cauerstr 11, D-91058 Erlangen, Germany

来源：

JOURNAL OF APPROXIMATION THEORY | 2016年 / 207卷

关键词：

Mellin transform; Mellin bandlimited functions; Riemann surfaces; Mellin derivatives; Paley-Wiener theorem; Bernstein inequality; DILATIONALLY INVARIANT TRANSFORMS; EXPONENTIAL-SAMPLING METHOD; FRACTIONAL CALCULUS; LAPLACE;

D O I：

10.1016/j.jat.2016.02.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we establish a version of the Paley-Wiener theorem of Fourier analysis in the frame of Mellin transforms. We provide two different proofs, one involving complex analysis arguments, namely the Riemann surface of the logarithm and Cauchy theorems, and the other one employing a Bernstein inequality here derived for Mellin derivatives. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：60 / 75

页数：16

共 25 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]

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

[5] The Foundations of Fractional Calculus in the Mellin Transform Setting with Applications [J].

Bardaro, Carlo ;

Butzer, Paul L. ;

Mantellini, Ilaria .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2015, 21 (05) :961-1017

[6] 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

[7] 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

[8]

Boas R. P., 1954, Entire Functions

[9] BERNSTEINS INEQUALITY AND NORM OF HERMITIAN OPERATORS [J].

BROWDER, A .

AMERICAN MATHEMATICAL MONTHLY, 1971, 78 (08) :871-&

[10] The classical and approximate sampling theorems and their equivalence for entire functions of exponential type [J].

Butzer, P. L. ;

Schmeisser, G. ;

Stens, R. L. .

JOURNAL OF APPROXIMATION THEORY, 2014, 179 :94-111

← 1 2 3 →