We study time-frequency localization operators of the form A12 a , where a is the symbol of the operator and φ1, φ2 are the analysis and synthesis windows, respectively. It is shown in [3] that a sufficient condition for A12 a ∈ Sp(L(R)), the Schatten class of order p, is that a belongs to the modulation space Mp,∞(R2d) and the window functions to the modulation space M1. Here we prove a partia...

Researching on the relationships among different multiple weighted type fractional Fourier transform (multi-WFRFT) schemes, we in this paper provide the modulation order relation of different multi-WFRFT in theory. Moreover, we also prove that the two matrix spaces (i.e., 4-WFRFT and multi-WFRFT) are equivalent. To apply multi-WFRFT into the wireless communication, we design the implementation ...

The main purpose of the paper is to give a characterization all compactly supported dual windows Gabor frame. As an application, we consider iterative procedure for approximation canonical window via on every step. In particular, allows have from certain modulation spaces or Schwartz space.

Pseudodifferential operators are an indispensable tool for the study of partial differential equations and are therefore a branch of classical analysis. In this chapter we offer an approach using time-frequency methods. In this approach time-frequency representations that are standard in signal analysis are used to set up the formalism of pseudodifferential operators, and certain classes of fun...

Several generalized Wallman type spaces are considered as well as various lattices of subsets therein. In particular, regularity of these lattices and consequences are investigated. Also considered are necessary and sufficient conditions for these lattices to be Lindel6f as well as replete, prime complete, and fully replete.

We prove the existence of designs of small size in a number of contexts. In particular our techniques can be applied to prove the existence of ndesigns on S of size Od(n d log(n)d−1).

A separable Banach space X contains l1 isomorphically if and only if X has a bounded fundamental total wc∗0-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded fundamental total wc∗0-biorthogonal system.

In this article we introduce the difference double sequence spaces 2`∞(∆, q), 2c(∆, q), 2c0(∆, q), 2c(∆, q), 2c0 (∆, q), 2c (∆, q) and 2c0 (∆, q) defined over a seminormed space (X, q), seminormed by q. We examine some topological and algebraic properties of these spaces like symmetricity, solidness, monotonocity, convergence free, nowhere densenes etc. We prove some inclusion results too.

In this paper, we obtain the existence and the uniqueness of common best proximity point theorems for non-self mappings between two subsets of a complex valued metric space satisfying certain contractive conditions. Our results supported by some examples.

To be written.