abstract. certain facts about frames and generalized frames (g- frames) are extended for the g-frames for hilbert c*-modules. it is shown that g-frames for hilbert c*-modules share several useful properties with those for hilbert spaces. the paper also character- izes the operators which preserve the class of g-frames for hilbert c*-modules. moreover, a necessary and suffcient condition is ob- ...

In this note‎, ‎we aim to show that several known generalizations of frames are equivalent to the continuous frame‎ ‎defined by Ali et al‎. ‎in 1993‎. ‎Indeed‎, ‎it is shown that these generalizations can be considered as an operator between two Hilbert spaces‎.

Let g be a continuous, compactly supported function on R such that the integer translates of g constitute a partition of unity. We show that the Gabor system (g, a, b), with window g and time-shift and frequency-shift parameters a, b > 0 has no lower frame bound larger than 0 if b = 2, 3, . . . and a > 0. In particular, (g, a, b) is not a Gabor frame if g is a continuous, compactly supported wa...

 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 real continuous functions $mathcal{R}L_tau $ as an $f$-ring. We show that $mathcal{R}L_{ tau}$ is actually a generali...

We introduce a new g-frame (singleton g-frame), g-orthonormal basis and g-Riesz basis and study corresponding notions in some other generalizations of frames.Also, we investigate duality  for some kinds of g-frames. Finally, we illustrate an example which provides a  suitable translation from discrete frames to Sun's g-frames.

in this note‎, ‎we aim to show that several known generalizations of frames are equivalent to the continuous frame‎ ‎defined by ali et al‎. ‎in 1993‎. ‎indeed‎, ‎it is shown that these generalizations can be considered as an operator between two hilbert spaces‎.

Generalized frames are an extension of frames in Hilbert  spaces and  Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an or...

In this paper we study the continuous dynamical sampling problem at infinite time in a complex Hilbert space H. We find necessary and sufficient conditions on bounded linear operator A∈B(H) set of vectors G⊂H, order to obtain that {etAg}g∈G,t∈[0,∞) is semi-continuous frame for if it possible discretize variable t still have also relate iteration etA G discrete (A′)n G′ an adequate A′ G′⊂H.

In this paper we introduce controlled *-g-frame and *-g-multipliers in Hilbert C*-modules and investigate the properties. We demonstrate that any controlled *-g-frame is equivalent to a *-g-frame and define multipliers for (C,C')- controlled*-g-frames .