Abstract As generalizations of g-frames and controlled frames, the theory has been deeply studied. This paper addresses dual in Hilbert spaces. We first present some equivalent characterizations g-frames. Then, we introduce concepts operator, get properties them. Finally, obtain for a given g-frame by method operator theory.

The notion of $k$-frames was recently introduced by Gu avruc ta in Hilbert  spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$-frame, so called c$k$-frame along with an atomic system ...

In this paper we consider  (extended) metaplectic representation of the  semidirect product  $G_{mathbb{J}}=mathbb{R}^{2d}timesmathbb{J}$  where $mathbb{J}$ is a closed subgroup of $Sp(d,mathbb{R})$, the symplectic group. We will investigate continuous representation frame on $G_{mathbb{J}}$. We also discuss the existence of duals for such frames and give several characterization for them. Fina...

The berization of aane systems via dual Gramian techniques, that was developed in previous papers of the authors, is applied here for the study of aane frames which have an aane dual system. Gramian techniques are also used to verify whether a dual pair of aane frames is a also a pair of bi-orthogonal Riesz bases. A general method for a painless derivation of a dual pair of aane frames from an ...

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.

Motivated by [B. Han and Q. Mo, Adv. Comp. Math. 18 (2003) 211-245] and [B. Han and Z. Shen, Constr. Approx. 29 (2009) 369-406], we propose dual two-direction frames in dual Sobolev spaces (H(R), H−s(R)), with s > 0. Based on the dual two-direction frames from a pair of two-direction refinable functions, dual multiwavelet frames with symmetry {Ψ(x) := (ψ 1(x), ψ 2(x)) T }`=1 and {Ψ̃(x) : = (ψ̃ 1(...

Progressive collapse is a condition where local failure of a primary structural component leads to the collapse of neighboring members and the whole structure, consequently. In this paper, the progressive collapse potential of seismically designed steel dual systems with buckling restrained braces is investigated using the alternate path method, and their performances are compared with those of...