Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. W...

in this paper, we give a necessary condition for function in l^2with its dual to generate a dual shearlet tight frame with respect to admissibility.

‎We present an application of the dual Gabor frames to image‎ ‎processing‎. ‎Our algorithm is based on finding some dual Gabor‎ ‎frame generators which reconstructs accurately the elements of the‎ ‎underlying Hilbert space‎. ‎The advantages of these duals‎ ‎constructed by a polynomial of Gabor frame generators are compared‎ ‎with their canonical dual‎.

In this paper, we introduced and characterized the controlled $g$-duals of a frame in separable Hilbert space $\mathcal{H}$ . Afterwards, obtained new $C$-controlled $g$-dual frames from given frames. addition, approximation for was defined some their properties were investigated. Finally, relationship between approximately dual $g$-dual.

Dual systems of steel moment frame and reinforced concrete shear wall have combined the advantages of steel frames and reinforced concrete shear wall. These walls have increased the lateral stiffness of steel frames and have reduced seismic demands on steel frames thus providing opportunities to use such system. In this research intermediate dual system of steel moment frame was chosen with int...

In This paper, we give a necessary condition for function in $L^2$ with its dual to generate a dual shearlet tight frame with respect to admissibility.

dual systems of steel moment frame and reinforced concrete shear wall have combined the advantages of steel frames and reinforced concrete shear wall. these walls have increased the lateral stiffness of steel frames and have reduced seismic demands on steel frames thus providing opportunities to use such system. in this research intermediate dual system of steel moment frame was chosen with int...

This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = {fi}i∈I and E = {ej}j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F in terms of the elements of E via a map a : I → G. A fundamental set of equalities are shown betwee...

‎we present an application of the dual gabor frames to image‎ ‎processing‎. ‎our algorithm is based on finding some dual gabor‎ ‎frame generators which reconstructs accurately the elements of the‎ ‎underlying hilbert space‎. ‎the advantages of these duals‎ ‎constructed by a polynomial of gabor frame generators are compared‎ ‎with their canonical dual‎.