Perturbation of sampling sets in irregular spline-type spaces
Jose Luis Romero
given at NuHAG seminar (13.02.07 10:30)
type: seminar talk
A spline-type space is a closed subspace of L^p possessing a Riesz basis generated by some translates of a W(C_0, L^1) function. We study the possibility of slightly perturbing a sampling set for such a space while retaining its sampling properties. We prove a general result on the possibility of doing so and in some particular cases give estimates on the allowed perturbation. We further explore the dependence of the sampling operator on the underlying sampling set and as a corollary we obtain a theoretical result on the existence of sampling sets optimising the sampling lower bound.
We will briefly discuss the applicability of these techniques to the problem of the instability of Riesz basis of translates under small perturbations of the translation points, deriving a sufficient criterion for the irregular shifts of a W(C_0, L^1) function to be a Riesz sequence.
There exists a preprint to this talk (with HGFei)