Generalized Jackson inequality in the space $L_2(\mathbb R^d)$ with Dunkl weight
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 109-118
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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.
Keywords:
root system, reflection group, Dunkl weight, Dunkl transform, best approximation, modulus of continuity, Jackson inequality.
@article{TIMM_2014_20_1_a10,
author = {V. I. Ivanov and Ha Thi Min Hue},
title = {Generalized {Jackson} inequality in the space $L_2(\mathbb R^d)$ with {Dunkl} weight},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {109--118},
publisher = {mathdoc},
volume = {20},
number = {1},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a10/}
}
TY - JOUR AU - V. I. Ivanov AU - Ha Thi Min Hue TI - Generalized Jackson inequality in the space $L_2(\mathbb R^d)$ with Dunkl weight JO - Trudy Instituta matematiki i mehaniki PY - 2014 SP - 109 EP - 118 VL - 20 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a10/ LA - ru ID - TIMM_2014_20_1_a10 ER -
%0 Journal Article %A V. I. Ivanov %A Ha Thi Min Hue %T Generalized Jackson inequality in the space $L_2(\mathbb R^d)$ with Dunkl weight %J Trudy Instituta matematiki i mehaniki %D 2014 %P 109-118 %V 20 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a10/ %G ru %F TIMM_2014_20_1_a10
V. I. Ivanov; Ha Thi Min Hue. Generalized Jackson inequality in the space $L_2(\mathbb R^d)$ with Dunkl weight. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 109-118. http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a10/