Optimal recovery from a finite set in Banach spaces of entire functions (Q734829)

In the papers [\textit{L. S. Maergoiz}, Dokl. Akad. Nauk, Ross. Akad. Nauk 356, No. 2, 161--165 (1997; Zbl 0973.32002); Sib. Mat. Zh. 41, No. 6, 1363--1375 (2000; Zbl 0970.32011)], conditions for optimal extrapolation of the Wiener class \(W_\sigma^2\) of entire functions are studied. In the present paper, the authors prove a theorem on extrapolation from a finite set in \(W_\pi^p\), where \(1<p<\infty\). The theorem still makes sense in purely algebraic context. Namely, let \(V\) be a \(\mathbb K\)-vector space, and let \(\{L_1,\dots, L_N\}\) be a linearly independent system of linear functionals on \(V\). The authors consider the problem of recovering a linear functional \(L\) on a subset \(U\) of \(V\) through \(L_1,\dots, L_N\).