Uniqueness in best one-sided \(L_ 1\)-approximation by algebraic polynomials on unbounded intervals (Q1262486)

The author takes up the study of the one-sided polynomial approximation for functions that are defined not necessarily on a compact interval only. The theorem proved here provides the existence of the best approximation and also shows the uniqueness of the approximation even over unbounded intervals for a certain class of functions. The theorem extends the corresponding result of \textit{R. Bojanic} and \textit{R. DeVore} [Enseign. Math., II. Ser. 12, 139-164 (1966; Zbl 0152.256)]. The author remarks that in general it is not possible to obtain the uniqueness exhibited here by just using the known transformation techniques.