Generalized Hankel shifts and exact Jackson Stechkin inequalities in L2
محورهای موضوعی : Mathematical Analysis
Tilektes Tileubayev
1
(MKМ, Faculty of Mathematics, Eurasian National University)
کلید واژه: Hankel transformations, Best approximation, modullus smoothness,
چکیده مقاله :
Abstract In this paper, we have solved several extremal problems of the best mean-square approximation of functions f, on the semi axis with a power-law weight. In the Hilbert space L2 with a power-law weight $t^{2\alpha+1}$ we obtain Jackson Stechkin type inequalities between the value E_{\sigma}(f) of the best approximation of a function f(t) by partial Hankel integrals S_{\sigma}(f) over the Bessel functions of the first kind and the kth-order generalized modulus of smoothness w_{k}(B^{r}f; t), where B is some second order differential operator.
Abstract In this paper, we have solved several extremal problems of the best mean-square approximation of functions f, on the semi axis with a power-law weight. In the Hilbert space L2 with a power-law weight $t^{2\alpha+1}$ we obtain Jackson Stechkin type inequalities between the value E_{\sigma}(f) of the best approximation of a function f(t) by partial Hankel integrals S_{\sigma}(f) over the Bessel functions of the first kind and the kth-order generalized modulus of smoothness w_{k}(B^{r}f; t), where B is some second order differential operator.
