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. The main purpose of the present paper is to prove approximation and commutatorproperties for projections mapping periodic Sobolev spaces onto shift-invariantspaces generated by a ?nite number of compactly supported functions. With these prerequisitesat hand and using certain localization techniques, we then characterize the stabilityof generalized Galerkin-Petrov schemes for solving periodic pseudodioeerential equations interms of elliptic type estimates of the numerical symbol....

Approximation and Commutator Properties of Projections onto Shift-Invariant Subspaces and Applications to Boundary Integral Equations