Perturbation Techniques in Irregular Spline-type Spaces

FEICHTINGER, HANS; MOLTER, URSULA M.; ROMERO, JOSE LUIS

International Journal of Wavelets, Multiresolution and Information Processing

World Scientific

Año: 2008 vol. 6 p. 249 - 277

0219-6913

In this article we study various perturbation techniques in thecontext of irregular spline-type spaces. We first present thesampling problem in this general setting and prove a generalresult on the possibility of perturbing sampling sets. This resultcan be regarded as an spline-type space analogue in the spirit ofKadec´s Theorem for bandlimited functions (see cite{ka64} andcite{le36}). We further derive some quantitative estimates on theamount by which a sampling set can be perturbed, and finally provea result on the existence of {em optimal} perturbations (with thestability of reconstruction being the optimality criterion).Finally, the techniques developed in the earlier parts of thearticle are used to study the problem of disturbing a basis for aspline-type space, in order to  derive a sufficient criterion fora space generated by irregular translations to be a spline-typespace.