The Bergman kernel and the green function

1. S. Bergman, “The kernel function and conformal mapping”,Math. Surveys, New York (1950).

2. N. Aronszajn, “Theory of reproducing kernels”,Trans. Am. Math. Soc.,68, 337–404 (1950).

   MATH  MathSciNet  Google Scholar 

3. N. N. Tarkhanov,The Parametrix Method in the Theory of Differential Complexes [in Russian], Novgorod (1990).

4. P. J. H. Hedenmalm “A computation of Green functions for the weighted biharmonic operators Δ|z|^−2αΔ, with α>−1”,U.U.D.M. Report (1992).

5. P. J. H. Hedenmalm, “Open problems in the function theory of the Bergman space”,U.U.D.M. Report (1992).

6. P. R. Garabedian, “A partial differential equation arising in conformal mapping”,Pacific J. Math.,1, 485–524 (1951).

   MATH  MathSciNet  Google Scholar 

7. J. Hadamard,Mémoire sur le Problème d'Analyse Relatif à l'Équilibre des Plaques Élastiques Encastrées, Paris (1908).

8. B. V. Shabat,Introduction to Complex Analysis. Part II [in Russian], Moscow (1976).

9. L. Hörmander,Analysis of Linear Differential Operators with Partial Derivatives [Russian Translation], Mir, Moscow (1986).

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10. V. A. Malyshev, “Hadamard conjecture and estimates of the Green function”,Algebra Analiz,4, 1–44 (1992).

    MATH  Google Scholar 

11. V. A. Malyshev,Elliptic Differential Inequalities [in Russian], Moscow (1994).

12. I. N. Vekua,New Methods of Solution of Elliptic Equations [in Russian], Moscow (1948).

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