We provide the appropriate common ‘(pre)framework’ for various central results of domain theory and topology, like the Lawson duality of continuous domains, the Hofmann–Lawson duality between continuous frames and locally compact sober spaces, the Hofmann–Mislove theorems about continuous semilattices of compact saturated sets, or the theory of stably continuous frames and their topological man...

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...

This thesis presents Gabor frames for L2(T) and for the space of periodic sequences Cp , as being analogue to Fourier series and the discrete Fourier transform. Results from the standard theory of Gabor frames for L2(R) are transferred to the periodic setting. This includes results about sampling Gabor systems and existence of Gabor frames. The interrelation of Gabor frames for the continuous s...

the generalization of p-frame in banach spaces is considered in this paper. the concepts of an $tilde{x}$-frame and a system conjugate to $tilde{x}$-frame were introduced. analogues of the results on the existence of conjugate system were obtained. the stability of $tilde{x}$-frame having a conjugate system is studied.

Wavelet and frames have become a widely used tool in mathematics, physics, and applied science during the last decade. In this article we discuss the construction of frames for L(R) using the action of closed subgroups H ⊂ GL(n,R) such that H has an open orbit O in R under the action (h, ω) 7→ (h) (ω). If H has the form ANR, where A is simply connected and abelian, N contains a co-compact discr...

Let G be a stratified Lie group and L be the sub-Laplacian on G. Let 0 6= f ∈ S(R). We show that Lf(L)δ, the distribution kernel of the operator Lf(L), is an admissible function on G. We also show that, if ξf(ξ) satisfies Daubechies’ criterion, then Lf(L)δ generates a frame for any sufficiently fine lattice subgroup of G.

We study the distribution of entanglement between modes of a free scalar field from the perspective of observers in relative acceleration. The degradation of entanglement due to the Unruh effect is analytically studied for two parties detecting a two-mode squeezed state in an inertial frame, in the cases of either one or both observers undergoing uniform acceleration. We find that for two non-i...