PERTURBATION TECHNIQUES IN IRREGULAR SPLINE-TYPE SPACES

Perturbation Techniques in Irregular Spline - Type Spaces Hans

In this article 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 an spline-type space analogue in the spirit of Kadec’s Theorem for bandlimited functions (see [14] and [15]). We further der...

Spline-type Spaces in Gabor Analysis

Explicit localization estimates for spline-type spaces

holds for every c ∈ `, and the functions {fk}k satisfy an spatial localization condition. In a spline-type space any function in f ∈ S has a unique expansion f = ∑ k ckfk. Moreover the coefficients are given by ck = 〈f, gk〉, where {gk}k ⊆ S is the dual basis, a set of functions characterized by the relation 〈gk, fj〉 = δk,j . These spaces provide a very natural framework for the sampling problem...

A Deconvolution Estimate and Localization in Spline-type Spaces

In this article some explicit estimates on the decay of the convolutive inverse of a sequence are proved. They are derived from the functional calculus for Sobolev algebras. Applications include localization in spline-type spaces and oversampling schemes.

Curvature continuous spline surfaces over irregular meshes

Conccpts and techniques for thc construction of spline surfaces over irregular meshes are developed and made concrete by exhibiting a family of 0 2 surface splines. These splines extend the B-spline paradigm for the construction of parametric piecewise polynomial surfaces to control_meshe9 with non quadrila.leral cells and mOre or fewer Lhan four cells meeting at a point. In particular, the mes...