We show that Hilbert–Schmidt operators can be used to define frame-like structures for $L^2(\mathbb{R}^d )$ over lattices in $\mathbb{R}^{2d} $ include multi-window Gabor frames as a special case. These are called g-frames

The concept of g-frame is a natural extension the frame. This article mainly discusses relationship between some special bounded linear operators and g-frames, characterizes properties g-frames. In addition, according to operator spectrum theory, eigenvalues are introduced into new expression best frame boundary given.

The familiar classical result that a continuous map from a space $X$ to a space $Y$ can be defined by giving continuous maps $varphi_U: U to Y$ on each member $U$ of an open cover ${mathfrak C}$ of $X$ such that $varphi_Umid U cap V = varphi_V mid U cap V$ for all $U,V in {mathfrak C}$ was recently shown to have an exact analogue in pointfree topology, and the same was done for the familiar cla...

in this paper we give some general results on the non-splitextension group $overline{g}_{n} = 2^{2n}{^{cdot}}sp(2n,2), ngeq2.$ we then focus on the group $overline{g}_{4} =2^{8}{^{cdot}}sp(8,2).$ we construct $overline{g}_{4}$ as apermutation group acting on 512 points. the conjugacy classes aredetermined using the coset analysis technique. then we determine theinertia factor groups and fischer...

For a locally compact group G and p ∈ (1,∞), we define Bp(G) to be the space of all coefficient functions of isometric representations of G on quotients of subspaces of Lp spaces. For p = 2, this is the usual Fourier–Stieltjes algebra. We show that Bp(G) is a commutative Banach algebra that contractively (isometrically, if G is amenable) contains the Figà-Talamanca–Herz algebra Ap(G). If 2 ≤ q ...

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...