Estimates of functionals by generalized moduli of continuity generated by the dunkl operators

Author:

Vinogradov O. L.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,General Mathematics,Statistics and Probability

Reference27 articles.

1. O. L. Vinogradov and V. V. Zhuk, “Estimates for functionals with a known finite set of moments in terms of deviations of operators constructed with the use of the Steklov averages and finite differences” [in Russian], Zap. Nauchn. Semin. POMI 392, 32–66 (2011).

2. C. F. Dunkl, “Differential-difference operators associated to reflection groups,” Trans. Amer. Math. Soc. 311, No. 1, 167–183 (1989).

3. M. Rösler, “Dunkl operators: theory and applications,” Lect. Notes Math. 1817, 93–135 (2003).

4. E. S. Belkina and S. S. Platonov, “Equivalence of K-functionals and modulus of smoothness constructed by generalized Dunkl translations” [in Russian], Izv. Vyssh. Uchebn. Zaved., Mat. No. 8, 3–15 (2008); English transl.: Russ. Math. 52, No. 8, 1-11 (2008).

5. K. Trimèche, “Transformation intégrale de Weyl et théorème de Paley — Wiener associés à un opérateur différentiel singulier sur (0,∞),” J. Math. Pures Appl. 60, 51–98 (1981).

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