If B < ∞ we call F = {fi}i∈I a Bessel sequence with Bessel bound B. If 0 < A ≤ B < ∞, then {fi}i∈I is a frame for K. If K 6= H we call {fi}i∈I a frame sequence in H. The largest A and the smallest B satisfying the above inequalities are called the optimal lower and upper frame bound and will be denoted A(F) and B(F) respectively. If A = B = λ we call this a λ-tight frame and if λ = 1 it is call...

and Applied Analysis 3 Proposition 1.3 see 4, 10 . A closed subspace X of L2 n is a reducing subspace if and only if X { f ∈ L2 n : supp ( f̂ ) ⊆ S } 1.5 for some measurable set S ⊆ n with ãS S. So, to be specific, one denotes a reducing subspace by L2 S ∨ instead of X. In particular, L2 n is a reducing subspace of L2 n . Definition 1.4 see 5–7 . Let B n be a subgroup of the integral affine grou...

We examine relations between popular variational methods in image processing and classical operator splitting methods in convex analysis. We focus on a gradient descent reprojection algorithm for image denoising and the recently proposed Split Bregman and alternating Split Bregman methods. By identifying the latter with the so-called DouglasRachford splitting algorithm we can guarantee its conv...

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...

In this paper we introduce and study Besselian $g$-frames. We show that the kernel of associated synthesis operator for a Besselian $g$-frame is finite dimensional. We also introduce $alpha$-dual of a $g$-frame and we get some results when we use the Hilbert-Schmidt norm for the members of a $g$-frame in a finite dimensional Hilbert space.

Weaving frames in separable Hilbert spaces have been recently introduced by Bemrose et al. to deal with some problems distributed signal processing and wireless sensor networks. In this paper, we study the notion of excess for woven prove that any two a space are same excess. We also show every frame large class duals is provided its redundant elements small enough norm. Also, try transfer prop...

In this paper we proved that every g-Riesz basis for Hilbert space $H$ with respect to $K$ by adding a condition is a Riesz basis for Hilbert $B(K)$-module $B(H,K)$. This is an extension of [A. Askarizadeh, M. A. Dehghan, {em G-frames as special frames}, Turk. J. Math., 35, (2011) 1-11]. Also, we derived similar results for g-orthonormal and orthogonal bases. Some relationships between dual fra...

Abstract In this article, we present the Laguerre wavelet exact Parseval frame method (LWPM) for two-dimensional flow of a rotating micropolar fluid in porous channel with huge mass transfer. This is governed by highly nonlinear coupled partial differential equations (PDEs) are reduced to ordinary (ODEs) using Berman's similarity transformation before being solved numerically method. We also co...

The goal is to extend Gleason’s notion of a frame function, which essential in his fundamental theorem quantum measurement, more general function acting on 1-tight, so-called, Parseval frames. We refer these functions as Gleason for reason our generalization that positive operator-valued measures (POVMs) are essentially equivalent frames and POVMs arise naturally measurement theory. prove under...