Dini–Lipschitz functions for the quaternion linear canonical transform

被引：0
作者：
A. Bouhlal
A. Achak
R. Daher
N. Safouane
机构：
[1] Labo Math Appli,Ecole Supérieure d’Education et Formation
[2] Faculty of Sciences,Department of Mathematics Faculty of Sciences Aïn Chock
[3] University Chouaib Doukkali,undefined
[4] University of Hassan II,undefined
来源：
Rendiconti del Circolo Matematico di Palermo Series 2 | 2021年 / 70卷
关键词：
Quaternion linear canonical transform; Lipschitz class; Dini–Lipschitz class; Titchmarsh theorem; -functional; 43A62; 42B10; 42B37;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper is an exposition of some results on calculation of the K-functional which have number of applications of interpolation theory. In particular some recent problems in image processing and singular integral operators require the computation of suitable K-functionals. In this paper we will give some results concerning the equivalence of a K-functional and the modulus of smoothness constructed by the generalized Steklov function. We mention here that we have generalized the Steklov’s function for Fourier transform to quaternion linear canonical transform. This paper generalizes also Titchmarsh’s theorem for measurable sets from complex domain to hyper complex domain by using quaternion algebras, associated with the quaternion linear canonical transform.
引用
收藏
页码：199 / 215
页数：16
相关论文
共 30 条
  • [1] Abouelaz A(2013)Fourier transform of Dini–Lipschitz functions in the space Roman. J. Math. Comput. Sci. 3 41-47
  • [2] Daher R(2017)Relation between quaternion Fourier transform and quaternion Wigner–Ville distribution associated with linear canonical transform J. Appl. Math. 2014 1-13
  • [3] El Hamma M(2016)A simplified proof of uncertainty principle for quaternion linear canonical transform Abstr. Appl. Anal. 11 19-24
  • [4] Bahri M(2013)On two-dimensional quaternion Wigner–Ville distribution J. Appl. Math. 8 3-15
  • [5] Fatimah SA(2015)Quaternion linear canonical transform application Glob. J. Pure Appl. Math. 121 143-157
  • [6] Bahri M(2008)Equivalence of K-functionnals andmodulus of smoothness constructed by generalized Dunkl translations Izv. Vyssh. Uchebn. Zaved. Mat. 1 1-6
  • [7] Ashino R(2003)Some equivalence theorems with K-functionals J. Approx. Theory 13 4401-4411
  • [8] Bahri M(2013)Dunkl transform of Dini–Lipschitz functions Electron. J. Math. Anal. Appl. 6 1185-1193
  • [9] Bahri M(2016)Fourier transforms of Dini–Lipschitz functions on rank 1 symmetric spaces Mediterr. J. Math. 247 675-688
  • [10] Belkina ES(2015)Polar linear canonical transform in quaternion domain J. Inf. Hiding Multimed. Sig. Process. 3 38-48
123