Yu. N. Subbotin's Method in the Problem of Extremal Interpolation in the Mean in the Space $L_p(\mathbb R)$ with Overlapping Averaging Intervals

On a uniform grid on the real axis, we study the Yanenko–Stechkin–Subbotin problem of extremal function interpolation in the mean in the space $L_p(\mathbb R)$, $1<p<\infty$, of two-way real sequences with the least value of the norm of a linear formally self-adjoint differential operator ${\mathcal L}_n$ of order $n$ with constant real coefficients. In case of even $n$, the value of the least norm in the space $L_p(\mathbb R)$, $1<p<\infty$, of the extremal interpolant is calculated exactly if the grid step $h$ and the averaging step $h_1$ are related by the inequality $h<h_1\leqslant 2h$.