Chebyshev Wavelet Analysis

被引：58

作者：

Guariglia, Emanuel ^{[1
]}

Guido, Rodrigo Capobianco ^{[1
]}

机构：

[1] Sao Paulo State Univ UNESP, Inst Biosci Letters & Exact Sci, Rua Cristovao Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil

来源：

JOURNAL OF FUNCTION SPACES | 2022年 / 2022卷

关键词：

D O I：

10.1155/2022/5542054

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with Chebyshev wavelets. We analyze their properties computing their Fourier transform. Moreover, we discuss the differential properties of Chebyshev wavelets due to the connection coefficients. Uniform convergence of Chebyshev wavelets and their approximation error allow us to provide rigorous proofs. In particular, we expand the mother wavelet in Taylor series with an application both in fractional calculus and fractal geometry. Finally, we give two examples concerning the main properties proved.

引用

页数：17

共 38 条

[1] New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators [J].

Akdemir, Ahmet Ocak ;

Butt, Saad Ihsan ;

Nadeem, Muhammad ;

Ragusa, Maria Alessandra .

MATHEMATICS, 2021, 9 (02) :1-11

[2]

Alibi H., 2010, Mathematical problems in Engineering, V2010, P17

[3] CHARACTERIZING THE LACUNARITY OF RANDOM AND DETERMINISTIC FRACTAL SETS [J].

ALLAIN, C ;

CLOITRE, M .

PHYSICAL REVIEW A, 1991, 44 (06) :3552-3558

[4] Numerical computation method in solving integral equations by using Chebyshev wavelet operational matrix of integration [J].

Babolian, E. ;

Fattahzadeh, F. .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 188 (01) :1016-1022

[5] Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration [J].

Babolian, E. ;

Fattahzadeh, F. .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 188 (01) :417-426

[6] Chebyshev wavelets approach for nonlinear systems of Volterra integral equations [J].

Biazar, J. ;

Ebrahimi, H. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 63 (03) :608-616

[7]

Cattani C., Fractional Dynamics, P1

[8] A CHARACTERIZATION OF THE CANTOR FUNCTION [J].

CHALICE, DR .

AMERICAN MATHEMATICAL MONTHLY, 1991, 98 (03) :255-258

[9]

Chan TF, 2005, IMAGE PROCESSING AND ANALYSIS, P1, DOI 10.1137/1.9780898717877

[10]

Daubechies I., 1992, 10 LECT WAVELETS

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