A new multivariate Toda hierarchy of nonlinear partial differential equations adapted to biorthogonal polynomials is discussed. This integrable associated with non-standard biorthogonality. Wave and Baker functions, linear equations, Lax Zakharov–Shabat KP type appropriate reductions, Darboux or spectral transformations, bilinear involving transformations are presented.

In this paper, we show that B-spline quarks and the associated quarklets fit into theory of biorthogonal multiwavelets. Quark vectors are used to define sequences subspaces [Formula: see text] which fulfill almost all conditions a multiresolution analysis. Under some special on parameters, they even satisfy those properties. Moreover, prove possess modulation matrices perfect reconstruction con...

The study of greedy approximation in the context convex optimization is becoming a promising research direction as algorithms are actively being employed to construct sparse minimizers for functions with respect given sets elements. In this paper we propose unified way analyzing certain kind greedy-type minimization on Banach spaces. Specifically, define class Weak Biorthogonal Greedy Algorithm...

We show how it is possible to diagonalize a certain class of homogeneous linear operators in a biorthogonal wavelet basis. Given a linear operator and a biorthogonal wavelet basis we construct a new biorthog-onal wavelet basis such that by analyzing a function in the new basis and multiplying the wavelet coeecients by a scale dependent factor we get the wavelet coeecients of the transformed fun...