A new description of orthogonal bases

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

Extended Jacobi and Laguerre Functions and their Applications

The aim of this paper is to introduce two new extensions of the Jacobi and Laguerre polynomials as the eigenfunctions of two non-classical Sturm-Liouville problems. We prove some important properties of these operators such as: These sets of functions are orthogonal with respect to a positive de nite inner product de ned over the compact intervals [-1, 1] and [0,1), respectively and also th...

Simultaneous Noise Suppression and Deconvolution with Best Bases and Minimum Description Criterion

In this paper, we proposed a method for simultaneous noise suppression and decon-volution. The signal estimation and denoising problem was converted into a problem of model selection by using minimum description length(MDL) criterion to choose the best bases through a library of orthogonal bases. Deconvolution was then done in this best bases domain(actually the wavelet packet coeecients) to ac...

New Bases for Polynomial-Based Spaces

Since it is well-known that the Vandermonde matrix is ill-conditioned, while the interpolation itself is not unstable in function space, this paper surveys the choices of other new bases. These bases are data-dependent and are categorized into discretely l2-orthonormal and continuously L2-orthonormal bases. The first one construct a unitary Gramian matrix in the space l2(X) while the late...

BIVARIATE LOCAL TRIGONOMETRIC BASES ON TRIANGULARPARTITIONSKai

We construct bivariate local trigonometric bases on a \two-overlapping" triangular grid. A main result is the description of various trigonometric bases on triangles, satisfying parity conditions at the edges. Moreover, we introduce folding operators for the triangular grid. From these results we derive assertions on Riesz stability and the bi-orthogonal basis.

New characterizations of fusion bases and Riesz fusion bases in Hilbert spaces

In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new denition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we dene the fusion biorthogonal sequence, Bessel fusion basis, Hil...