Some algorithms for the dynamic reconstruction of inputs

For the weight \(v_k \left( x \right) = \prod _{\alpha \in \mathbb{R}_ + } \left| {\left( {\alpha ,x} \right)} \right|^{2k\left( \alpha \right)}\) defined by a positive subsystem R ₊ of a finite root system R ? ? ^d and by a function k(α): R → ?₊ invariant under the reflection group generated by R, a sharp Jackson inequality in L ₂(? ^d ) is proved.