Positive harmonic function: Difference between revisions

Revision as of 00:48, 22 December 2011

Revision as of 00:49, 22 December 2011

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A holomorphic function ''f'' on the unit disk with ''f''(0) = 1 has positive real part if and only if there is a probability measure μ on the unit circle such that

:<math> f(z) ={1\over 2\pi} \int_0^{2\pi} {1 + e^{-i\theta}z\over 1 -e^{-i\theta}z} \, d\mu(\theta).</math>

This follows from the previous theorem because: