The orthonormal basis generated by a wavelet of L(R) has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions where we consider arbitrary dilation matrices. The resulting basis of L(R) is called the multiwavelet packet basis. The concept of wavelet frame packet is also generalized...

Sequences of unit vectors for which the Kaczmarz algorithm always converges in Hilbert space can be characterized in frame theory by tight frames with constant 1. We generalize this result to the context of frames and bases. In particular, we show that the only effective sequences which are Riesz bases are orthonormal bases. Moreover, we consider the infinite system of linear algebraic equation...

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In this paper, model sets for linear time-invariant discrete-time systems spanned by fixed orthonormal bases are studied. It is shown that the Fourier series of the system transfer function with respect to these bases converges uniformly on the unit circle if the frequency response of the system is Dini-Lipschitz continuous.

We construct a monomial basis of the positive part U of the quantized enveloping algebra associated to a finite–dimensional simple Lie algebra. As an application we give a simple proof of the existence and uniqueness of the canonical basis of U. 0. Introduction In [L1], Lusztig showed that the positive part U of the quantized enveloping algebra associated to a finite–dimensional simple Lie alge...

The aim of this paper is to provide complementary quantitative extensions of two results of H.S. Shapiro on the time-frequency concentration of orthonormal sequences in L2(R). More precisely, Shapiro proved that if the elements of an orthonormal sequence and their Fourier transforms are all pointwise bounded by a fixed function in L2(R) then the sequence is finite. In a related result, Shapiro ...

The aim of this paper is to provide complementary quantitative extensions of two results of H.S. Shapiro on the time-frequency concentration of orthonormal sequences in L(R). More precisely, Shapiro proved that if the elements of an orthonormal sequence and their Fourier transforms are all pointwise bounded by a fixed function in L(R) then the sequence is finite. In a related result, Shapiro al...