More on fast decreasing trigonometric polynomials - D. Leviatan; O.V. Motorna; I.O. Shevchuk (Researches in Mathematics)
In a recent paper, for a fixed $m\in\mathbb N$, we introduced trigonometric polynomials $$ L_n(x):=\frac1{h^m}\underbrace{\int_{-h/2}^{h/2}…\int_{-h/2}^{h/2}}_{m\,\text{times}}J_n(x+t_1+…+t_m)\,dt_1…\,dt_m, $$ where $J_n$ is a Jackson-type kernel. In the current paper we show that $L_n$ and its first $m-1$ derivatives provide approximation to the $B$-spline of degree $m-1$ and its respective derivatives.