Good morning to you all,

any genius in the house ? does anybody know how to solve this ?? please help. thank you

Ps: f_k is f sub k

f^ is f hat

f^(n) = nth Fourier coeffcient of f

suppose that {f_k } is a sequence where k goes from 0 to infinity, is a sequence of Riemann integrable functions on the interval [0; 1] such that

INTEGRAL FROM 0 TO 1 OF |f_k (x) - f(x)| dx -> 0 as k -> infinity

Show that f^_k(n) -> f^(n) uniformly in n as k -> infinity