The notion of operator-valued frames (OVFs) by Kaftal et al. (Trans Am Math Soc 361(12):6349–6385, 2009) and G-frames Sun (J Anal Appl 322(1):437–452, 2006) do not include all generalizations notions for Hilbert spaces. For this purpose, we introduce the weak (weak OVFs) which covers known Theory weak-OVFs is more demanding than theory OVFs due to following: One, frame operator may factor anoth...

Block frames called directional analytic discrete cosine frames (DADCFs) are proposed for sparse image representation. In contrast to conventional overlapped frames, the DADCFs require a reduced amount of 1) computational complexity, 2) memory usage, and 3) global access. These characteristics strongly required current high-resolution processing. Specifically, we propose two based on tra...

We present a general method for construction of frames {ψI}I∈D for Triebel-Lizorkin and Besov spaces, whose nature can be prescribed. In particular, our method allows for constructing frames consisting of rational functions or more general functions which are linear combinations of a fixed (small) number of shifts and dilates of a single smooth and rapidly decaying function θ such as the Gaussi...

The deepest and most difficult question in Fusion Frame Theory is the construction of fusion frames with added properties for specific applications. In frame theory we have a powerful tool introduced by Benedetto and Fickus [1] called frame potentials (See [5] for a deep analysis of frame potentials). Frame potentials are a valuable tool for showing the existence of frames with certain specifie...

‎In this paper‎, ‎two iterative methods are constructed to solve the operator equation $ Lu=f $ where $L:Hrightarrow H $ is a bounded‎, ‎invertible and self-adjoint linear operator on a separable Hilbert space $ H $‎. ‎ By using the concept of frames of subspaces‎, ‎which is a generalization of frame theory‎, ‎we design some  algorithms based on Galerkin and Richardson methods‎, ‎and then we in...

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...

Let g ∈ L2(R) be a compactly supported function, whose integertranslates {Tkg}k∈Z form a partition of unity. We prove that for certain translationand modulation parameters, such a function g generates a Gabor frame, with a (non-canonical) dual generated by a finite linear combination h of the functions {Tkg}k∈Z; the coefficients in the linear combination are given explicitly. Thus, h has compac...

Abstract In this work, we analyze Gabor frames for the Weyl--Heisenberg group and wavelet extended affine group. Firstly, give necessary sufficient conditions existence of nonstationary translates. Using these conditions, prove from We present a representation functions in closure linear span frame sequence terms Fourier transform window functions. show that canonical dual translates has same s...

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...

algebraic frames are generalizations of fourier transforms on locally compact abelian groups in the sense that the family of vectors forming the frame are replaced by a family of unbounded linear functionals. the paper studies the indexing measure space of the algebraic frames; as the investigation narrows down to the class of lower semiframes, more relations are revealed between the discret...