A class of extremal functions and trigonometric polynomials (Q1354679)

The author generalizes results of \textit{J. D. Vaaler} [Bull. Am. Math. Soc., New Ser. 12, 183-216 (1985; Zbl 0575.42003)]. He constructs two classes of extremal approximating entire functions of finite exponential type, which give good approximation for a specific set of functions along the real line. The first class provides majorants and minorants, while the second class minimizes the \(L^1\)-norm on the real line. As applications extremal trigonometric polynomials are constructed and an inequality about almost trigonometric polynomials is obtained.