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...

This paper presents MATLAB programs for generating the coefficients of the lowpass analysis filter corresponding to orthonormal wavelet analyses. One of the programs generates the famous Daubechies maxflat wavelets, and a second generates the Daubechies complex symmetric orthonormal wavelets. The remaining two programs generate the space of all orthonormal wavelets in terms of parameterizations...

Glossary 5 Introduction 6 Definition of Wavelets 7 Definition of Filters 8 Multi-Resolution Analysis 9 Wavelet Decomposition and Reconstruction 10 Refinable Functions 11 Compactly Supported Orthonormal Wavelets 12 Parameterization of Orthonormal Wavelets 13 Biorthogonal Wavelets 14 Prewavelets 15 Tight Wavelet Frames 16 Tight Wavelet Frames over Bounded Domain 17 q-Dilated Orthonormal Wavelets ...

The most simple (and useful) linear expansions for Hilbert spaces are the ones that are based on orthonormal bases. Recall that a set of vectors {xα} in an inner product space (IPS) X is said to be orthogonal if xα ⊥ xβ whenever α 6= β. In addition, if each vector in the set is normalized to have unit norm then the set is said to be orthonormal. Orthonormal sets have many nice properties that m...

In this paper, model sets for continuous{time linear time invariant systems that are spanned by xed pole orthonormal bases are investigated. These bases gen-eralise the well known Laguerre and Kautz bases. It is shown that the obtained model sets are complete in all of the Hardy spaces H p ((); 1 p < 1 and the right half plane algebra A(() provided that a mild condition on the choice of basis p...

Orthonormal systems in commutative L2 spaces can be used to classify Banach spaces. When the system is complete and satisfies certain norm condition the unconditionality with respect to the system characterizes Hilbert spaces. As a noncommutative analogue we introduce the notion of unconditionality of operator spaces with respect to orthonormal systems in noncommutative L2 spaces and show that ...