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The purpose of this note is to present an extension and an alternative proof to Theorem 1.3 from G. Battle (Appl. Comput. Harmonic Anal. 4 (1997) 119–146). This extension applies to wavelet Bessel set...
Stability Theorems for Fourier Frames and Wavelet Riesz Bases
Frames Riesz basis nonharmonic series wavelets
2015/9/29
In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type co...
We discuss a method for curve estimation based on n noisy
data; one translates the empirical wavelet coecients towards the origin by
an amount p
2 log(n) =p
n. The method is nearly minimax for...
Central limit theorem for the robust log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context
Central limit theorem the robust log-regression wavelet estimation
2010/11/23
In this paper, we study robust estimators of the memory parameter d of a (possibly) non stationary Gaussian time series with generalized spectral density f. This generalized spectral density is chara...
This paper addresses the construction of wavelet frame from a {\it frame multiresolution analysis} ({\bf FMRA}) associated with a dilation matrix of determinant $\pm 2$. The dilation matrices of deter...
General Solutions of Matrix Extension Associated with Multiple Channel Biorthogonal Wavelet Filters
matrix extension refinement equation biorthogonal wavelet
2007/12/11
This paper is concerned with seeking the general solutions of matrix equation $\widetilde{M}(\xi)M^*(\xi)=I_s$ for the construction of multiple channel biorthogonal wavelets, provided that some specia...