A sampling theorem and Wintner's results on Fourier coefficients (Q1108521)

It is proved that if f(z)\(\in H\) 1(U), where U is the unit open disc and \(f'(z)\in Lip_ 1\) on \(| z| =1\), then the Taylor coefficients of f(z) are given by \(c_ n=\sum^{\infty}_{k=1}\mu (k)/kn\sum^{kn}_{m=1}f(\omega \quad m_{kn}),\) where \(\omega_{kn}=e^{2\pi_ i/kn}\) and \(\mu\) is the Möbius function.