PERTURBATION TECHNIQUES IN IRREGULAR SPLINE-TYPE SPACES

摘要

In this paper we study various perturbation techniques in the context of irregular spline-type spaces. We first present the sampling problem in this general setting and prove a general result on the possibility of perturbing sampling sets. This result can be regarded as a spline-type space analogue in the spirit of Kadec's Theorem for bandlimited functions (see Refs. 14 and 15). We further derive some quantitative estimates on the amount by which a sampling set can be perturbed, and finally prove a result on the existence of optimal perturbations (with the stability of reconstruction being the optimality criterion). Finally, the techniques developed in the earlier parts of the paper are used to study the problem of disturbing a basis for a spline-type space, in order to derive a sufficient criterion for a space generated by irregular translations to be a spline-type space.