On the Paley-Wiener theorem in the Mellin transform setting

JOURNAL OF APPROXIMATION THEORY

卷:207

Article

Bardaro, Carlo¹  Butzer, Paul L.²  Mantellini, Ilaria¹  Schmeisser, Gerhard³ 

[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

关键词: Mellin transform;    Mellin bandlimited functions;    Riemann surfaces;    Mellin derivatives;    Paley-Wiener theorem;    Bernstein inequality;   

DOI  :  10.1016/j.jat.2016.02.010

来源: Elsevier

【 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.

【 授权许可】

Free