Equivalence of <i>K</i>-Functionals and Modulus of Smoothness Generated by a Generalized Dunkl Operator on the Real Line
نویسندگان
چکیده
منابع مشابه
Equivalence of K-functionals and modulus of smoothness for fourier transform
In Hilbert space L2(Rn), we prove the equivalence between the mod-ulus of smoothness and the K-functionals constructed by the Sobolev space cor-responding to the Fourier transform. For this purpose, Using a spherical meanoperator.
متن کاملequivalence of k-functionals and modulus of smoothness for fourier transform
in hilbert space l2(rn), we prove the equivalence between the mod-ulus of smoothness and the k-functionals constructed by the sobolev space cor-responding to the fourier transform. for this purpose, using a spherical meanoperator.
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On the real line, the Dunkl operators are differential-difference operators introduced in 1989 by Dunkl [1] and are denoted by Λα, where α is a real parameter > −1/2. These operators are associated with the reflection group Z2 on R. The Dunkl kernel Eα is used to define the Dunkl transform α which was introduced by Dunkl in [2]. Rösler in [3] shows that the Dunkl kernels verify a product formul...
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ژورنال
عنوان ژورنال: Advances in Pure Mathematics
سال: 2015
ISSN: 2160-0368,2160-0384
DOI: 10.4236/apm.2015.56035