Approximation Properties of Sobolev Splines and the Construction of Compactly Supported Equivalents

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

Construction of multivariate compactly supported prewavelets in L2 space and pre-Riesz bases in Sobolev spaces

We give a new constructive method for finding compactly supported prewavelets in L2 spaces in the multivariate setting. This method works for any dimensional space. When this method is generalized to the Sobolev space setting, it produces a pre-Riesz basis for Hs(IR) which can be useful for applications. AMS(MOS) Subject Classifications: Primary 42C15, Secondary 42C30

Construction of compactly supported biorthogonal wavelets: I

This paper presents a construction of compactly supported dual functions of a given box spline in L2(IR ). In particular, a concrete method for the construction of compactly supported dual functions of bivariate box splines of increasing smoothness is provided. Key-Words:multivariate biorthogonal wavelets, multivariate wavelets, box splines, matrix extension

Construction of compactly supported biorthogonal wavelets

This paper presents a construction of compactly supported biorthogonal spline wavelets in L2(IR ). In particular, a concrete method for the construction of bivariate compactly supported biorthogonal wavelets from box splines of increasing smoothness is provided. Several examples are given to illustrate the method. Key-Words:multivariate biorthogonal wavelets, multivariate wavelets, box splines,...

Characterization of Sobolev Spaces of Arbitrary Smoothness Using Nonstationary Tight Wavelet Frames

In this paper we shall characterize Sobolev spaces of an arbitrary order of smoothness using nonstationary tight wavelet frames for L2(R). In particular, we show that a Sobolev space of an arbitrary fixed order of smoothness can be characterized in terms of the weighted `2-norm of the analysis wavelet coefficient sequences using a fixed compactly supported nonstationary tight wavelet frame in L...