On estimates for the quaternion linear canonical transform in the space L2(R2,H)

This paper is an exposition of some estimates which have a number of applications to interpolation theory. In particular some recent problems in image processing and singular integral operators require the computation of suitable estimates. In Abilov et al. (Comput Math Math Phys 48:2146, 2008) , Ab...

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Published inRendiconti del Circolo matematico di Palermo Vol. 73; no. 4; pp. 1701 - 1714
Main Authors Achak, A., Akhlidj, A., Daher, R., Jaafari, A.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2024
Subjects
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Quaternion linear canonical transform
Dini–Lipschitz class
Lipschitz class
42B10
43A62
42B37
Titchmarsh theorem
Estimates
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Abstract This paper is an exposition of some estimates which have a number of applications to interpolation theory. In particular some recent problems in image processing and singular integral operators require the computation of suitable estimates. In Abilov et al. (Comput Math Math Phys 48:2146, 2008) , Abilov et al. proved two useful estimates for the Fourier transform in the space of square integral multivariable functions on certain classes of functions characterized by the generalized continuity modulus, and these estimates are proved by Abilov for only two variables, using a translation operator. The purpose of this paper is to study these estimates for measurable sets from complex domain to hyper complex domain by using quaternion algebras, associated with the quaternion linear canonical transform, constructed by the generalized Steklov function.
AbstractList This paper is an exposition of some estimates which have a number of applications to interpolation theory. In particular some recent problems in image processing and singular integral operators require the computation of suitable estimates. In Abilov et al. (Comput Math Math Phys 48:2146, 2008) , Abilov et al. proved two useful estimates for the Fourier transform in the space of square integral multivariable functions on certain classes of functions characterized by the generalized continuity modulus, and these estimates are proved by Abilov for only two variables, using a translation operator. The purpose of this paper is to study these estimates for measurable sets from complex domain to hyper complex domain by using quaternion algebras, associated with the quaternion linear canonical transform, constructed by the generalized Steklov function.
Author Achak, A.
Daher, R.
Jaafari, A.
Akhlidj, A.
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  organization: Department of Mathematics, Faculty of Sciences Aïn Chock, University of Hassan II
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Cites_doi 10.1007/BF03018622
10.1016/j.camwa.2008.05.032
10.1016/j.sigpro.2013.08.008
10.1017/S0305004100055638
10.1063/1.1665805
10.1007/978-1-4757-0872-1
10.1007/s00009-017-0989-4
10.1007/s00009-016-0752-2
10.1007/s00006-007-0037-8
10.1007/s00006-019-1020-x
10.1134/S096554250812004X
10.1364/JOSA.60.001168
10.1016/j.sigpro.2009.09.030
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Keywords Quaternion linear canonical transform
Dini–Lipschitz class
Lipschitz class
42B10
43A62
42B37
Titchmarsh theorem
Estimates
Language English
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Snippet This paper is an exposition of some estimates which have a number of applications to interpolation theory. In particular some recent problems in image...
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StartPage 1701
SubjectTerms Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Title On estimates for the quaternion linear canonical transform in the space L2(R2,H)
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