Geodesic
Weighted biharmonic green functions for rational weights
Glasgow mathematical journal, Tome 41 (1999) no. 2, pp. 239-269

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We present an algorithm for computing the Green function of the weighted biharmonic operator Δ|P′|−2Δ on the unit disc (with Dirichlet boundary conditions) for rational functions P. As an application, we show that if P is a Blaschke product with two zeros α1, α2 the Green function is positive if and only if |(α1−α2)/(1−{\bar α}1α2)|≤{2 \over 7}{\sqrt 10}, and also obtain an explicit formula for the Green function of the operator Δ|G|−2Δ, where G is the canonical zero-divisor of a finite zero set on the Bergman space. 
Engliš, Miroslav. Weighted biharmonic green functions for rational weights. Glasgow mathematical journal, Tome 41 (1999) no. 2, pp. 239-269. doi: 10.1017/S0017089599970957
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     author = {Engli\v{s}, Miroslav},
     title = {Weighted biharmonic green functions for rational weights},
     journal = {Glasgow mathematical journal},
     pages = {239--269},
     year = {1999},
     volume = {41},
     number = {2},
     doi = {10.1017/S0017089599970957},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089599970957/}
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