In areas of geometric modeling and wavelets, one often needs to construct a compactly supported reenable function with suucient regularity which is fundamental for interpolation (that means, (0) = 1 and () = 0 for all 2 Z s nf0g). Low regularity examples of such functions have been obtained numerically by several authors and a more general numerical scheme was given in RiS1]. This paper present...

In areas of geometric modeling and wavelets, one often needs to construct a compactly supported reenable function with suucient regularity which is fundamental for interpolation (that means, (0) = 1 and () = 0 for all 2 Z s nf0g). Low regularity examples of such functions have been obtained numerically by several authors and a more general numerical scheme was given in RiS1]. This paper present...

Based on the method for constructing tight wavelet frames of [RS2], we show that one can construct, for any dilation matrix, and in any spatial dimension, tight wavelet frames generated by compactly supported functions with arbitrarily high smoothness. AMS (MOS) Subject Classifications: Primary 42C15, Secondary 42C30

In this correspondence, we generalize the theory of compactly supported biorthogonal two-channel wavelet bases to M -channel. A sufficient condition for the M -channel perfect reconstruction filter banks to constructM -channel biorthogonal bases of compactly supported wavelets is derived. It is shown that the construction of biorthogonal M -channel wavelet bases is equivalent to the design of a...

We show that compactly supported functions with sufficient smoothness and enough vanishing moments can serve as analyzing vectors for shearlet coorbit spaces. We use this approach to prove embedding theorems for subspaces of shearlet coorbit spaces resembling shearlets on the cone into Besov spaces. Furthermore, we show embedding relations of traces of these subspaces with respect to the real a...

For any 2×2 dilation matrix with integer entries and | detA| = 2, we construct a family of smooth compactly supported tight wavelet frames with three generators in L2(R). Our construction involves some compactly supported refinable functions, the Oblique Extension Principle and a slight generalization of a theorem of Lai and Stöckler. Estimates for the degrees of smoothness are given. With the ...

In this paper we investigate the effective content of the structure theorem for the space E ′ of distributions with compact support. We show that each of the four characterisations of the space of distributions with compact support given in the structure theorem (below) gives rise to an effective domain representation of E ′. To show that the structure theorem has effective content, we study th...

A hierarchical scheme is presented for smoothly interpolating scattered data with radial basis functions of compact support. A nested sequence of subsets of the data is computed efficiently using successive Delaunay triangulations. The scale of the basis function at each level is determined from the current density of the points using information from the triangulation. The method is rotational...