References

Bateman, H. and A. Erdelyi, 1974. Higher Transcendental Functions. McGraw-Hill, New York, USA.,.

Belkina, E.S. and S.S. Platonov, 2008. Equivalence of K-functionals and modulus of smoothness constructed by generalized Dunkl translations. Russ. Math., 52: 1-11.
CrossRef  |  Direct Link  |  

Dai, F., 2003. Some equivalence theorems with K-functionals. J. Approximation Theory, 121: 143-157.
Direct Link  |  

Ditzian, Z. and V. Totik, 1987. Moduli of Smoothness. Springer, Berlin, Germany,.

Dunkl, C.F., 1989. Differential-difference operators associated to reflection groups. Trans. Am. Math. Soc., 311: 167-183.
Direct Link  |  

Konovalov, V.N., D. Leviatan and V.E. Maiorov, 2008. Approximation by polynomials and ridge functions of classes of s-monotone radial functions. J. Approximation Theory, 152: 20-51.
CrossRef  |  Direct Link  |  

Konovalov, V.N., D. Leviatan and V.E. Maiorov, 2009. Approximation of Sobolev classes by polynomials and ridge functions. J. Approximation Theory, 159: 97-108.
Direct Link  |  

Lofstrom, J. and J. Peetre, 1969. Approximation theorems connected with generalized translations. Math. Ann., 181: 255-268.
CrossRef  |  Direct Link  |  

Maiorov, V. and A. Pinkus, 1999. Lower bounds for approximation by MLP neural networks. Neurocomputing, 25: 81-91.
Direct Link  |  

Maiorov, V., 2003. On best approximation of classes by radial functions. J. Approximation Theory, 120: 36-70.
Direct Link  |  

Rosler, M., 2003. Dunkl Operators: Theory and Applications. In: Orthogonal Polynomials and Special Functions, Koelink, E. and W.V. Assche (Eds.). Springer, Berlin, Germany, ISBN: 978-3-540-44945-4, pp: 93-135.

Salem, N.B. and S. Kallel, 2004. Mean-periodic functions associated with the Dunkl operators. Integral Transforms Spec. Functions, 15: 155-179.
Direct Link  |  

Xu, Z. and F. Cao, 2004. The essential order of approximation for neural networks. Sci. China Ser. F. Inf. Sci., 47: 97-112.
CrossRef  |  Direct Link  |