Solution
= Solution
The substitution $x=\cos\theta$ identifies the weighted norm with the $L^2(0,\pi)$ norm of $f(\cos\theta)$. Completeness of cosine Fourier <series> therefore makes the Chebyshev partial sums converge in $\|\cdot\|_w$.
= Solution
The substitution $x=\cos\theta$ identifies the weighted norm with the $L^2(0,\pi)$ norm of $f(\cos\theta)$. Completeness of cosine Fourier <series> therefore makes the Chebyshev partial sums converge in $\|\cdot\|_w$.