We study Sobolev type estimates for the approximation order resulting from using strictly positive deenite kernels to do interpolation on the n-sphere. The interpolation knots are scattered. Our approach partly follows the general theory of Golomb and Weinberger 10] and related estimates of 6]. These error estimates are then based on series expansions of… (More)
In this paper a large class of universal windows for Gabor frames (Weyl-Heisenberg frames) is constructed. These windows have the fundamental property that every overcritical rectangular lattice generates a Gabor frame. Likewise, every undercritical rectangular lattice generates a Riesz sequence.
When a Cardinal B-spline of order greater than 1 is used as the scaling function to generate a multiresolution approximation of L 2 = L 2 (IR) with dilation integer factor M ≥ 2, the standard " matrix extension " approach for constructing compactly supported tight frames has the limitation that at least one of the tight frame generators does not annihilate… (More)
A new class of differential operators on the simplex is introduced, which define weighted Sobolev norms and whose eigenfunctions are orthogonal polynomials with respect to Jacobi weights. These operators appear naturally in the study of quasi-interpolants which are intermediate between Bernstein– Durrmeyer operators and orthogonal projections on polynomial… (More)
We study totally positive (TP) functions of finite type and exponential B-splines as window functions for Gabor frames. We establish the connection of the Zak transform of these two classes of functions and prove that the Zak transforms have only one zero in their fundamental domain of quasi-periodicity. Our proof is based on the variation-diminishing… (More)