Exponential box-like splines on nonuniform grids

Exponential box - like splines on nonuniform

Box-like Splines With Nonuniform Stepsize

We construct a polynomial spline similar to the box spline, except that we relax the condition that its knots are spaced uniformly in each direction. The recurrence relation for this spline is a generalization of the recurrence relations for the box spline and univariate B-spline. The construction generalizes to exponential-polynomial splines [5]. §

An Upper Bound on the Approximation Power of Principal Shift-invariant Spaces

An upper bound on the Lp-approximation power (1 p 1) provided by principal shift-invariant spaces is derived with only very mild assumptions on the generator. It applies to both stationary and non-stationary ladders, and is shown to apply to spaces generated by (exponential) box splines, polyharmonic splines, multiquadrics, and Gauss kernel.

Translates of Exponential Box Splines and Their Related Spaces

Exponential box splines (SB-splines) are multivariate compactly supported functions on a regular mesh which are piecewise in a space St spanned by exponential polynomials. This space can be defined as the intersection of the kernels of certain partial differential operators with constant coefficients. The main part of this paper is devoted to algebraic analysis of the space H of all entire func...

Characterizations of multivariate differences and associated exponential splines

The subject of this investigation is the class of difference functionals—linear combinations of finitely many function and/or derivative evaluations—which annihilate the nullspace of a certain constant coefficient differential operator. Any such functional can be viewed as an integral-differential operator whose Peano kernel is a compactly supported exponential spline. Besides extending some ea...