WIAS Preprint No. 372, (1997)

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


  • Prössdorf, Siegfried
  • Schult, Jörg

2010 Mathematics Subject Classification

  • 41A05 41A15 41A17 45B05 45E10 45L10 45M10 65N12 65N35 65N38


  • Approximation property, commutator property, superapproximation property, periodic pseudodifferential equations, multiscaling functions, multiwavelets, splines with multiple knots, Strang-Fix condition, Galerkin-Petrov methods




The main purpose of the present paper is to prove approximation and commutator properties for projections mapping periodic Sobolev spaces onto shift-invariant spaces generated by a finite number of compactly supported functions. With these prerequisites at hand and using certain localization techniques, we then characterize the stability of generalized Galerkin-Petrov schemes for solving periodic pseudodifferential equations in terms of elliptic type estimates of the numerical symbol. Moreover, we establish optimal convergence rates for the approximate solutions with respect to the Sobolev norms.

Appeared in

  • J. Integral Equations Appl., 10, (1998), No. 4, pp. 417-444

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