On the Nörlund Method of Signal Processing Involving Coifman Wavelets

We consider on real line R a space of signals which are p-power (1 ≤ p ≤∞ ) Lebesgue integrable with weight w(x) = (1 - x)α (1 + x)β , ( α, β > -1) on [-1, 1] R. A subspace χabNvof Xabvis recognized by restricting the types of signals, so that the signals are represented by Jacobi Polynomials. Then by the derivability of Jacobi polynomials, we reach to the conclusion that the signals of the subspace XαβNv can be represented by the Coifman wavelets. The method involves the N rlund summation of Fourier-Jacobi expansions and the properties of Jacobi polynomials in [--1, 1] R

A note on the extension of a family of biorthogonal Coifman wavelet systems

Wavelet systems with a maximum number of balanced vanishing moments are known to be extremely useful in a variety of applications such as image and video compression. Tian and Wells recently created a family of such wavelet systems, called the biorthogonal Coifman wavelets, which have proved valuable in both mathematics and applications. The purpose of this work is to establish along with direct proofs a very neat extension of Tian and Wells' family of biorthogonal Coifman wavelets by recovering other “missing” members of the biorthogonal Coifman wavelet systems.