On the stability of the L^2 projection and the quasiinterpolant in the space of smooth periodic splines

06/16/2021

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by   D. C. Antonopoulos V. A. Dougalis, et al.

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In this paper we derive stability estimates in L^2- and L^∞- based Sobolev spaces for the L^2 projection and a family of quasiinterolants in the space of smooth, 1-periodic, polynomial splines defined on a uniform mesh in [0,1]. As a result of the assumed periodicity and the uniform mesh, cyclic matrix techniques and suitable decay estimates of the elements of the inverse of a Gram matrix associated with the standard basis of the space of splines, are used to establish the stability results.