ISSN 1683-3414 (Print)   •   ISSN 1814-0807 (Online)
   Log in


Address: Vatutina st. 53, Vladikavkaz,
362025, RNO-A, Russia
Phone: (8672)23-00-54





Dear authors!
Submission of all materials is carried out only electronically through Online Submission System in personal account.
DOI: 10.23671/VNC.2018.3.18031

Some Estimates for the Generalized Fourier Transform Associated with the Cherednik-Opdam Operator on \(\mathbb{R}\)

El Ouadih S. , Daher R. , Lafdal H. S.
Vladikavkaz Mathematical Journal 2018. Vol. 20. Issue 3.
In the classical theory of approximation of functions on \(\mathbb{R}^+\), the modulus of smoothness are basically built by means of the translation operators \(f \to f(x+y)\). 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 \(T^{(\alpha,\beta)}\) in \(L^{2}_{\alpha,\beta}(\mathbb{R})\). For this purpose, we use a generalized translation operator.
Keywords: Cherednik-Opdam operator, generalized Fourier transform, generalized translation.
Language: English Download the full text  
For citation: El Ouadih S., Daher R., Lafdal H. S. Some Estimates for the Generalized Fourier Transform Associated with the Cherednik-Opdam Operator on \(\mathbb{R}\), Vladikavkazskij matematicheskij zhurnal [Vladikavkaz Math. J.], vol. 20, no. 2, pp. 78-86. DOI 10.23671/VNC.2018.3.18031
+ References

← Contents of issue
  | Home | Editorial board | Publication ethics | Peer review guidelines | Latest issue | All issues | Rules for authors | Online submission systems guidelines | Submit manuscript |