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Galerkin-Petrov methods for Bergman space Toeplitz operators. (English) Zbl 0779.65036

Authors’ summary: The convergence of several Galerkin-Petrov methods is established, including polynomial collocation and analytic element collocation methods, for Toeplitz operators on the Bergman space of the unit disk. In particular, it is shown that such methods converge if the basis and test functions (or the collocation points) own certain circular symmetry, whereas unfortunate choice of the basis and test parameters produces nonconvergent Galerkin-Petrov methods.
Reviewer: G.Vainikko (Tartu)

MSC:

65J10 Numerical solutions to equations with linear operators
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
65R20 Numerical methods for integral equations
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
30C40 Kernel functions in one complex variable and applications
47A50 Equations and inequalities involving linear operators, with vector unknowns
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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