We consider best m-term approximation in Lp(R) with wave packets generated from a single refinable function. The main examples of such wave packets are orthonormal wavelets or more generally tight wavelet frames based on an MRA (so-called framelets). The approximation classes associated with best m-term approximation in Lp(R) with such wave packets are completely characterized in terms of Besov...

in this paper, we determine the structure of the space of multipliers of the range of a composition operator cφ that induces by the conditional expectation between two lp() spaces.

We consider best m-term approximation in Lp(R) with wave packets generated by a single refinable function. The main examples of wave packets are orthonormal wavelets, or more generally wavelet frames based on a multiresolution analysis (so-called framelets). The approximation classes associated with best m-term approximation in Lp(R) for a large class of wave packets are completely characterize...

We investigate the existence of infinite dimensional Banach spaces having rigid sets with an infinite number of elements. Among Banach lattices, examples are provided by infinite dimensional AM -spaces as well as for some abstract Lp-spaces, 1 ≤ p < ∞.

In this paper, the cost and income efficiency models have been considered with regard to the multiple objective programming structures. For finding the efficient points in purposed MOLP problem, some various methods like Lexicography & the weighted sum can be used. So by introducing the MOLP problem the cost & income efficiencies will be achieved. In the present study, the MOLP problem is conve...

Schur's test for integral operators states that if a kernel K:X×Y→C satisfies ∫Y|K(x,y)|dν(y)≤C and ∫X|K(x,y)|dμ(x)≤C, then the associated operator is bounded from Lp(ν) into Lp(μ), simultaneously all p∈[1,∞]. We derive variant of this result which ensures acts boundedly on (weighted) mixed-norm Lebesgue spaces Lwp,q, p,q∈[1,∞]. For non-negative kernels our criterion sharp; is, only it spaces. ...

The problem of countably quasi-barrelledness of weighted spaces of continuous functions, of which there are no results in the general setting of weighted spaces, is tackled in this paper. This leads to the study of quasi-barrelledness of weighted spaces in which, unlike that of Ernst and Schnettler (1986), though with a similar approach, we drop the assumption that the weighted space has a fund...

We introduce weighted moduli of smoothness for functions f ∈ Lp[−1, 1]∩Cr−1(−1, 1), r ≥ 1, that have an (r−1)st absolutely continuous derivative in (−1, 1) and such that φf (r) is in Lp[−1, 1], where φ(x) = (1−x). These moduli are equivalent to certain weighted D-T moduli, but our definition is more transparent and simpler. In addition, instead of applying these weighted moduli to weighted appr...