Need help with connection of theorems
I need help with using/derive fejer-cesaro approximation to prove weierstrass approximation theorem: every continuous function on [a,b] can be approximate uniformly by polynomials.
How do I find a continuous function g on an interval of fejer-cesaro that is isomorphic to f:[a,b] in weierstrass approximation theorem?
The fejer-cesaro given: An(x)=(So+S2+S3+.......+S(n-1))/N with the fourier series nth partial sum Sf(x)=Summation of Cke^(jkx) where k=-n to n and x is in [0,2pi]
and I need help to prove An(x) is a polynomial.
I would be very appreciate if someone can give me hints of find g and show that An(x) is a polynomial.