Suppose that $f(x)\in C[0,1]$. Can we find an infinite sequence $\{a_n\}$ such that
$$ \lim_{N\rightarrow \infty} ||f(x)-\sum_{n=0}^{N}a_n \cos3^n \pi x||_\infty=0$$?
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Sign up to join this communitySuppose that $f(x)\in C[0,1]$. Can we find an infinite sequence $\{a_n\}$ such that
$$ \lim_{N\rightarrow \infty} ||f(x)-\sum_{n=0}^{N}a_n \cos3^n \pi x||_\infty=0$$?