Some estimates for the generalized Fourier transform associated with the Cherednik-Opdam operator on r

Автор: El Ouadih Salah, Daher Radouan, Lafdal Hamad Sidi

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 3 т.20, 2018 года.

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In the classical theory of approximation of functions on R+, the modulus of smoothness are basically built by means of the translation operators f→f(x+y). As the notion of translation operators was extended to various contexts (see [2] and [3]), many generalized modulus of smoothness have been discovered. Such generalized modulus of smoothness are often more convenient than the usual ones for the study of the connection between the smoothness properties of a function and the best approximations of this function in weight functional spaces (see [4] and [5]). In [1], Abilov et al. proved two useful estimates for the Fourier transform in the space of square integrable functions on certain classes of functions characterized by the generalized continuity modulus, using a translation operator. In this paper, we also discuss this subject. More specifically, we prove some estimates (similar to those proved in [1]) in certain classes of functions characterized by a generalized continuity modulus and connected with the generalized Fourier transform associated with the differential-difference operator T(α,β) in L2α,β(R). For this purpose, we use a generalized translation operator.

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Cherednik-opdam operator, generalized fourier transform, generalized translation

Короткий адрес: https://sciup.org/143168775

IDR: 143168775   |   DOI: 10.23671/VNC.2018.3.18031

Список литературы Some estimates for the generalized Fourier transform associated with the Cherednik-Opdam operator on r

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