An extremal problem for trigonometric polynomials
An extremal problem for trigonometric polynomials
Let $T_{n}(x)=\sum _{k=0}^{n}(a_{k}\cos kx+b_{k}\sin kx)$ be a trigonometric polynomial of degree $n.$ The problem of finding $C_{np},$ the largest value for $C$ in the inequality $\max \{\left | a_{0}\right | ,\left | a_{1}\right | ,...,\left | a_{n}\right | ,\left | b_{1}\right | ,...,\left | b_{n}\right | \}$ $\leq (1/C)\left \| …