A CLASS OF EXTREMAL-FUNCTIONS AND TRIGONOMETRIC POLYNOMIALS

In this paper we present two classes of extremal approximating functio ns. These functions have the property that they are entire, have finit e exponential type, and provide excellent approximations along the rea l line for a specific set of functions. One class of functions provide s majorants and minorants, while the other class minimizes the L(1)-no rm on the real line. As applications we construct extremal trigonometr ic polynomials and obtain an inequality involving almost periodic trig onometric polynomials. (C) 1997 Academic Press.