We discuss extremal problems for non-negative trigonometric polynomials with prescribed zeros. The general result is used to refine a former theorem of Fejér concerning upper bounds of those polynomials near to a zero. Another application deals with the coefficient problem for typically real (algebraic) polynomials.
Cite this article
Stephan Ruscheweyh, Non-Negative Trigonometric Polynomials with Constraints. Z. Anal. Anwend. 5 (1986), no. 2, pp. 169–177