Abstract:

The convergence of several Galerkin--Petrov methods, including polynomial collocation and analytic element collocation methods of Toeplitz operators on Dirichlet space, is established. In particular, it is shown that such methods converge if the basis and test function own certain circular symmetry.

Key words: Galerkin-Petrov methods, polynomial collocation, analytic element collocation,
Toeplitz operators, Dirichlet space