Geodesic
Dunkl theory and Jackson inequality in $L_2(\mathbb R^d)$ with power weight
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 180-192
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We prove a sharp Jackson inequality in $L_2(\mathbb R^d)$ with the weight $v_k(x)=\prod_{\alpha\in\mathbb R_+}|(\alpha,x)|^{2k(\alpha)}$ defined by the positive subsystem $R_+$ of a finite system of roots $R\subset\mathbb R^d$ and by a function $k(\alpha)\colon R\to\mathbb R_+$ invariant under the reflection group generated by $R$.
Keywords: reflection group, Dunkl transform, best approximation, modulus of continuity, Jackson inequality. 
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A. V. Ivanov; V. I. Ivanov. Dunkl theory and Jackson inequality in $L_2(\mathbb R^d)$ with power weight. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 180-192. http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a16/

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