In this paper it is shown how false operator responses due to missing or uncertain data can be sig-niicantly reduced or eliminated. Perhaps the most well-known of such eeects are the variousèdge eeects' which invariably occur at the edges of the input data set. Further, it is shown how operators having a higher degree of selectivity and higher tolerance against noise can be constructed using si...

Schürmann's theory of quantum Lévy processes, and more generally the theory of quantum stochastic convolution cocycles, is extended to the topological context of compact quantum groups and operator space coalge-bras. Quantum stochastic convolution cocycles on a C *-hyperbialgebra, which are Markov-regular, completely positive and contractive, are shown to satisfy coalgebraic quantum stochastic ...

We study a smoothing effect of a non-linear degenerate parabolic problem, the Vlasov-Poisson-Fokker-Planck system, in three dimensions. We prove that a solution gives rise actually to very smooth macroscopic density and force field for positive time. This is obtained by analyzing the effect of the Fokker-Planck kernel on the force term in the Vlasov equation and using classical convolution ineq...

where ∆ is the Laplace operator. Here σ > 0 is a constant (the diffusion constant). It has dimensions of distance squared over time, so H0 has dimensions of inverse time. The operator exp(−tH0) for t > 0 is an self-adjoint integral operator, which gives the solution of the heat or diffusion equation. Here t is the time parameter. It is easy to solve for this operator by Fourier transforms. Sinc...

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...

This paper is concerned with the source-type of integral equation to compute the electromagnetic scattering by an inhomogeneous 3D object in a planar layered medium in the frequency domain. By decomposing the scattered field into a particular and a general constituent, the structure of the integral operator of the integral equation is constructed. The particular constituent represents the scatt...

einstein, möbius, and proper velocity gyrogroups are relativistic gyrogroups that appear as three different realizations of the proper lorentz group in the real minkowski space-time $bbb{r}^n$. using the gyrolanguage we study their gyroharmonic analysis. although there is an algebraic gyroisomorphism between the three models we show that there are some differences between them. our study focus ...

We describe numerical implementations of the discrete convolution operator and the derivative operator in the framework of nonstandard wavelet decomposition of linear operators. In both cases, the operator matrix and the input vector are rst expanded in a compactly supported discrete wavelet basis. Then the scale-wise eeect of the expanded operator matrix on the input vector is computed. The co...

In recent years, Fourier multiplier theorems in vector–valued function spaces have found many applications in embedding theorems of abstract function spaces and in theory of differential operator equations, especially in maximal regularity of parabolic and elliptic differential–operator equations. Operator–valued multiplier theorems in Banach–valued function spaces have been discussed extensive...