Two-wavelet theory in Weinstein setting

New results on the continuous Weinstein wavelet transform

We consider the continuous wavelet transform [Formula: see text] associated with the Weinstein operator. We introduce the notion of localization operators for [Formula: see text]. In particular, we prove the boundedness and compactness of localization operators associated with the continuous wavelet transform. Next, we analyze the concentration of [Formula: see text] on sets of finite measure. ...

Model Theory a Palimpsest of Phil 516 by Scott Weinstein

Simultaneous Wavelet Deconvolution in Periodic Setting

The paper proposes a method of deconvolution in a periodic setting which combines two important ideas, the fast wavelet and Fourier transform-based estimation procedure of Johnstone et al. [J. Roy. Statist. Soc. Ser. B 66 (2004) 547] and the multichannel system technique proposed by Casey and Walnut [SIAM Rev. 36 (1994) 537]. An unknown function is estimated by a wavelet series where the empiri...

Functional Wavelet Deconvolution in a Periodic Setting

We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover initial or boundary conditions on the basis of observations from a noisy solution of a partial differential equation. In the case when it is observed at a f...

Wavelet deconvolution in a periodic setting

Deconvolution problems are naturally represented in the Fourier domain, whereas thresholding in wavelet bases is known to have broad adaptivity properties. We study a method which combines both fast Fourier and fast wavelet transforms and can recover a blurred function observed in white noise with O{n log.n/2} steps. In the periodic setting, the method applies to most deconvolution problems, in...