Local theory of the collocation method for the approximate solution of singular integral equations. I (Q802295)

First, the authors describe an elegant abstract setting for analyzing projection methods for solving linear operator equations: The convergence of a projection method turns out to be equivalent to the invertibility of the coset of the sequence of projected operators in a certain factor algebra of a Banach algebra formed in a natural way from the projectional scheme; this invertibility in turn can be characterized by a local principle. The authors use these results to prove convergence of collocation methods for solving systems of singular integral equations with piecewise continuous coefficients.