Generalized Jackson inequality in the space $L_2(\mathbb R^d)$ with Dunkl weight

V. I. Ivanov ; Ha Thi Min Hue

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 109-118

Résumé

A generalized modulus of continuity is defined in the space $L_2(\mathbb R^d)$ with Dunkl weight by means of an arbitrary zero-sum sequence of complex numbers. A sharp generalized Jackson inequality is proved for this modulus and the best approximations by entire functions of exponential spherical type. This inequality was earlier proved by S. N. Vasil'ev in the weightless case.

Détail

Keywords: root system, reflection group, Dunkl weight, Dunkl transform, best approximation, modulus of continuity, Jackson inequality.

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