The Bergman kernel and the Green function. (English. Russian original) Zbl 0927.32001
J. Math. Sci., New York 87, No. 2, 3366-3380 (1997); translation from Zap. Nauchn. Semin. POMI 221, 145-166 (1995).
See the review in Zbl 0885.32021.
MSC:
| 32A25 | Integral representations; canonical kernels (Szegő, Bergman, etc.) |
| 32A37 | Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) |
Citations:
Zbl 0885.32021References:
| [1] | S. Bergman, ”The kernel function and conformal mapping”,Math. Surveys, New York (1950). · Zbl 0040.19001 |
| [2] | N. Aronszajn, ”Theory of reproducing kernels”,Trans. Am. Math. Soc.,68, 337–404 (1950). · Zbl 0037.20701 · doi:10.1090/S0002-9947-1950-0051437-7 |
| [3] | N. N. Tarkhanov,The Parametrix Method in the Theory of Differential Complexes [in Russian], Novgorod (1990). · Zbl 0758.58002 |
| [4] | P. J. H. Hedenmalm ”A computation of Green functions for the weighted biharmonic operators {\(\Delta\)}|z|{\(\alpha\)}{\(\Delta\)}, with {\(\alpha\)}>”,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). · Zbl 0045.05102 · doi:10.2140/pjm.1951.1.485 |
| [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). |
| [10] | V. A. Malyshev, ”Hadamard conjecture and estimates of the Green function”,Algebra Analiz,4, 1–44 (1992). · Zbl 0779.35034 |
| [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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