The convolution theorem (Hájek [8]) characterizes the weak limit of any regular estimator as a convolution of two independent components. One is an optimal achievable part and another is a noise. Therefore, the optimal estimator is one without the noise part in its weak limit, which is a deeper characterization than the Cramer-Rao bound. However, this result is derived under the assumption that...

This paper deals with convolution setting at boundary regions for 1D convolution computed during recursive Gaussian and Gabor filtering as well as staged Gabor filtering computed more efficiently as modulation, recursive Gaussian, and demodulation. These are established fast approximations to their filters. Until recently, all the three applications of recursive filters suffered from distortion...

This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

Scattering data The scattering data associated with a LODE usually consists of a reflection coefficient which is a function of the spectral parameter λ, a finite number of constants λj that correspond to the poles of the transmission coefficient in the upper half complex plane, and the bound-state norming constants whose number for each bound-state pole λj is the same as the order of that pole....

When analyzing linear systems of equations, the most important indicator of potential instability is the condition number of the matrix. For a convolution matrix W formed from a series w (where Wij wi-, + ,, 1 5 i j + 1 5 k , W,j = 0 otherwise), this condition number defines the stabirity of the deconvolution process. For the larger convolution matrices commonly encountered in practice, direct ...

In this paper we consider a discrete version of the Bernoulli convolution problem traditionally studied via functional analysis. We develop an algorithm which bounds the Bernoulli sequences, and we give a significant improvement on the best known bound.

Hill MR, Fried I, Koch C. Quantification and classification of neuronal responses in kernel-smoothed peristimulus time histograms. J Neurophysiol 113: 1260–1274, 2015. First published December 4, 2014; doi:10.1152/jn.00595.2014.—Peristimulus time histograms are a widespread form of visualizing neuronal responses. Kernel convolution methods transform these histograms into a smooth, continuous pr...

Making use of a convolution structure, we introduce a new class of analytic functions defined in the open unit disc and investigate coefficient estimates, distortion bounds and the results on integral transform. Further we investigate the neighbourhood results and partial sums. 2000 Mathematics Subject Classification: 30C45.