We consider the aff(1)-module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the Lie superalgebra aff(1) with coefficients in space Dλ,ν;µ of bilinear differential operators acting on weighted densities. We study also the super analogue of this problem getting the same results.

The large usage of multimedia applications on internet and mobiles has increased the demand of compressed data, as to reduce the bandwidth requirement and transmission time. So block based method for video compression is getting more importance due to its effectiveness and easy implementation. Fractal video compression follows the property of self-similarity. The weighted finite automata exploi...

— In wireless broadband systems the available time, frequency and spatial diversity can be exploited using complex space-time-frequency codes. However, in order to retain a flexible scheme with low complexity we prefer a concatenated system where a channel code picks up time and frequency diversity and a simple orthogonal design is used to obtain spatial diversity. The channel needs to be const...

We establish a weighted Lp boundedness of a parametric Marcinkiewicz integral operator ρ Ω,h if Ω is allowed to be in the block space B (0,−1/2) q (Sn−1) for some q > 1 and h satisfies a mild integrability condition. We apply this conclusion to obtain the weighted Lp boundedness for a class of the parametric Marcinkiewicz integral operators ∗,ρ Ω,h,λ and ρ Ω,h,S related to the Littlewood-Paley ...

Weighted shifts on directed trees are a decade-old generalisation of classical shift operators in the sequence space ℓ2. In this paper we introduce joint backward extension property (JBEP) for classes weighted trees. If class satisfies JBEP, existence common within family rooted does not depend additional structure big tree (of fixed depth). We decide whether several have JBEP. For subnormal or...

We study when the operator f(Bw) is chaotic in the sense of Devaney on a Köthe echelon sequence space, where Bw is a weighted backward shift and f(z) = ∑∞ j=0 fjz j is a formal power series.