Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the convolution of an exponential B-spline with a compact-support distribution. As a direct consequence of this factorization theorem, we show t...

For the Schoenberg B-splines, interesting relations between their functional representation, Dirichlet averages and difference operators are known. We use these relations to extend the B-splines to an arbitrary (infinite) sequence of knots and to higher dimensions. A new Fourier domain representation of the multidimensional complex B-spline is given. 1. Complex B-Splines Complex B-splines are a...

This work is one of many that are devoted to the further investigation of local interpolating polynomial splines of the fifth order approximation. Here, new polynomial and trigonometrical basic splines are presented. The main features of these splines are the following; the approximation is constructed separately for each grid interval (or elementary rectangular), the approximation constructed ...

Dirichlet averages of multivariate functions are employed for a derivation of basic recurrence formulas for the moments of multivariate Dirichlet splines. An algorithm for computing the moments of multivariate simplex splines is presented. Applications to hypergeometric functions of several variables are discussed. Introduction. In [9], H.B. Curry and I.J. Schoenberg have pointed out that univa...

We present a novel method named truncated hierarchical unstructured splines (THU-splines) that supports both local h-refinement and quadrilateral meshes. In THU-spline construction, an mesh is taken as the input control mesh, where degenerated-patch [20] adopted in irregular regions to define $$C^1$$ -continuous bicubic splines, whereas regular only involve $$C^2$$ B-splines. Irregular are then...

The first type of pseudo-splines were introduced by [Daubechies, Han, Ron and Shen, 2003] (DHRS) to construct tight framelets with desired approximation orders via the unitary extension principle of [Ron and Shen, 1997]. In the spirit of the first type of pseudo-splines, we introduce here a new type (the second type) of pseudo-splines to construct symmetric or antisymmetric tight framelets with...