MathDB

Let

C=\bigcup_{N=1}^{\infty}C_N,

where

C_N

denotes the set of 'cosine polynomials' of the form

f(x)=1+\sum_{n=1}^Na_n\cos(2\pi nx)

for which:
(i)

f(x)\ge 0

for all real

x,

and (ii)

a_n=0

whenever

n

is a multiple of

3.

Determine the maximum value of

f(0)

f

ranges through

C,

and prove that this maximum is attained.

Problem Statement