The Green function for the weighted biharmonic operator \(\Delta(1-| z|^2)^{-\alpha}\Delta\), and factorization of analytic functions

DOI10.1007/BF02355831zbMath0909.31004OpenAlexW2321890117MaRDI QIDQ1376857

Serguei Shimorin

Publication date: 1 October 1998

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/68574

zbMATH Keywords

Green's functionBergman spaceanalytic functionexplicit formulaweighted biharmonic operator

Mathematics Subject Classification ID

Entire functions of one complex variable (general theory) (30D20) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)

Related Items (5)

THE ESSENTIAL NORMS OF COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES ⋮ Construction of Green functions for weighted biharmonic operators. ⋮ An integral formula in weighted Bergman spaces ⋮ Extremal functions in weighted Bergman spaces ⋮ The Green functions for weighted biharmonic operators of the form \(\Delta\omega^{-1}\Delta\) in the unit disk

Cites Work

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• Contractive zero-divisors in Bergman spaces
• Differential equations for the magnetic confinement of a plasma
• Extremal functions in invariant subspaces of Bergman spaces
• A partial differential equation arising in conformal mapping
• On generation of solutions of the biharmonic equation in the plane by conformal mappings
• Remark on the preceding paper of Charles Loewner
• A factorization theorem for square area-integrable analytic functions.
• On the failure of optimal factorization for certain weighted bergman spaces
• On a Question of Hadamard Concerning Super‐Biharmonic Functions

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