Commutator Properties for Periodic Splines Original Research Article

Commutator properties are established for periodic splines with distinct uniformly spaced knots (on uniform meshes) operated on by certain pseudo-differential 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.