Mellin analysis and its basic associated metric-applications to sampling theory

被引：13

作者：

Bardaro, C. ^{[1
]}

Butzer, P. L. ^{[2
]}

Mantellini, I. ^{[1
]}

Schmeisser, G. ^{[3
]}

机构：

[1] Univ Perugia, Dept Math & Comp Sci, Perugia, Italy

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

[3] FAU Erlangen Nuremberg, Dept Math, D-91058 Erlangen, Germany

来源：

ANALYSIS MATHEMATICA | 2016年 / 42卷 / 04期

关键词：

Mellin transform; Mellin derivative; Mellin-Bernstein space; Mellin distance; approximate sampling formula; approximate reproducing kernel formula; Mellin-Bernstein inequality; DILATIONALLY INVARIANT TRANSFORMS; EXTENSIONS; FORMULA; LAPLACE;

D O I：

10.1007/s10476-016-0401-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper a notion of functional "distance" in the Mellin transform setting is introduced and a general representation formula is obtained for it. Also, a determination of the distance is given in terms of Lipschitz classes and Mellin-Sobolev spaces. Finally applications to approximate versions of certain basic relations valid for Mellin band-limited functions are studied in details.

引用

页码：297 / 321

页数：25

共 22 条

[1]

Adams R.A., 1975, Sobolev Spaces

[2]

[Anonymous], 1994, TABLES INEGRALS SERI

[3]

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

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