Commutator properties for periodic splines
Commutator properties are established for periodic splines with distinct uniformly spaced knots (on uniform meshes) operated on by certain pseudodifferential operators. The commutation involves the operations of multiplication by a smooth function and application of a discrete version of orthogonal projection obtained by using a quadrature rule (which need integrate only constants exactly) to approximate the inner product. The results mirror a well known super--approximation property of splines multiplied by smooth functions.
scientific article; zbMATH DE number 1278844
scientific article