Nikolskii type inequality for cardinal splines (Q1286716)

Nikolski type inequality for restriction on \(R\) of entire functions of exponential type \(\sigma>0\), which are in \(L_p(R) , p>0\) is known [see e.g. \textit{S. M. Nikolskij}, Approximation of functions of several variables and imbedding theorems (1975; Zbl 0307.46024)]. The author obtains an analogous inequality for cardinal splines of degree \(m\), smoothness \(C^{m-1}\) and with mesh intervals of length \(h\) centred at \(nh+{{1}\over{2}}mh\), \(n\in\mathbb{Z}\), which are in \(L_p(R)\).