Generalized Hankel shifts and exact Jackson{Stechkin inequalities in L2

Theory of Approximation and Applications

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 02 آبان 1402

نوع مقاله: Research Articles

نویسنده

Tilektes tileubayev^*

МКМ, математический факультет, Евразийский Национальный Университет

چکیده

Abstract In this paper, we have solved several extremal problems of the best mean-square
approximation of functions f, on the semiaxis 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 rst kind and the kth-order generalized modulus of smoothnes$w_{k}(B^{r}f; t), where B is some
second{order dierential operator.

کلیدواژه‌ها

Best approximation؛ modullus smoothness؛ Hankel transformations