Positive harmonic function: Difference between revisions

Revision as of 04:15, 23 December 2011

Revision as of 04:16, 23 December 2011

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:<math>\sum_m\sum_n a_{m-n} \lambda_m\overline{\lambda_n} =\int_0^{2\pi} \left|\sum_{n=}^N \lambda_n e^{-in\theta}\right|^2 \, d\mu(\theta) \ge 0.</math>

Conversely, setting λ_''n'' &nbsp;=&nbsp;''z''^''n'',

:<math>\sum_{m=0}^\infty\sum_{n=0}^\infty a_{m-n} \lambda_m\overline{\lambda_n} = 2(1-|z|^2) \,\Re\, f(z).</math>

==See also==

*[[Bochner's theorem]]