Positive harmonic function: Difference between revisions

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Carathéodory's positivity criterion for holomorphic functions: Coefficients in the taylor series of f are not the same like covariance coefficients a / fourier coefficients respektive....that was very misleading
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Then
 
:<math> f_n(re^{i\theta}) = {1\over 2\pi}\int_0^{2\pi} {1-r^2\over 1-2r\cos(\theta-\varphi) + r^2 }\, f_n(\varphi)\,d\phivarphi =\int_0^{2\pi}{1-r^2\over 1-2r\cos(\theta-\varphi) + r^2 } d\mu_n(\varphi)</math>
 
where