The talk is concerned with the existence of multiple knot periodic splines satisfying general Hermite interpolation conditions and their approximation power in Sobolev spaces. The key for such results are necessary and sufficient conditions for the existence of interpolating cardinal splines which have knots in Z.
In an extended first part of the talk a fundamental application of periodic splines to the discretization of periodic pseudo differential operators by the qualocation method is presented in an introductory style.
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