The Mellin-Parseval formula and its interconnections with the exponential sampling theorem of optical physics

被引：22

作者：

Bardaro, Carlo ^{[1
]}

Butzer, Paul L. ^{[2
]}

Mantellini, Ilaria ^{[1
]}

机构：

[1] Univ Perugia, Dept Math & Comp Sci, I-06123 Perugia, Italy

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

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2016年 / 27卷 / 01期

关键词：

Mellin transform; Mellin bandlimited functions; exponential sampling theorem; reproducing kernel formula; Mellin-Parseval formula; APPROXIMATION; CONVERGENCE; OPERATORS;

D O I：

10.1080/10652469.2015.1087401

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish a Mellin version of the classical Parseval formula of Fourier analysis in the case of Mellin bandlimited functions, and its equivalence with the exponential sampling formula (ESF)of signal analysis, in which the samples are not equally spaced apart as in the classical Shannon theorem, but exponentially spaced. Two quite different examples are given illustrating the truncation error in the ESF. We employ Mellin transform methods for square-integrable functions.

引用

页码：17 / 29

页数：13

共 20 条

[1] Convergence and rate of approximation in BVφ (R+N) for a class of Mellin integral operators [J].

Angeloni, Laura ;

Vinti, Gianluca .

RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, 2014, 25 (03) :217-232

[2]

Angeloni L, 2013, DIFFER INTEGRAL EQU, V26, P655

[3]

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

[4] 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

[5] On Mellin convolution operators: a direct approach to the asymptotic formulae [J].

Bardaro, Carlo ;

Mantellini, Ilaria .

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2014, 25 (03) :182-195

[6] 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

[7] Vitali-type theorems for filter convergence related to vector lattice-valued modulars and applications to stochastic processes [J].

Boccuto, Antonio ;

Candeloro, Domenico ;

Sambucini, Anna Rita .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 419 (02) :818-838

[8]

Brychkov Y., 1992, Multidimensional Integral Transformations

[9] Seven pivotal theorems of Fourier analysis, signal analysis, numerical analysis and number theory: their interconnections [J].

Butzer, P. L. ;

Dodson, M. M. ;

Ferreira, P. J. S. G. ;

Higgins, J. R. ;

Schmeisser, G. ;

Stens, R. L. .

BULLETIN OF MATHEMATICAL SCIENCES, 2014, 4 (03) :481-525

[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

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