In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and ...

In this paper, we give some conditions under which the finite sum of continuous $g$-frames is again a continuous $g$-frame. We give necessary and sufficient conditions for the continuous $g$-frames $Lambda=left{Lambda_w in Bleft(H,K_wright): win Omegaright}$ and $Gamma=left{Gamma_w in Bleft(H,K_wright): win Omegaright}$ and operators $U$ and $V$ on $H$ such that $Lambda U+Gamma V={Lambda_w U+Ga...

Given an arbitrary sequence of elements ξ = { n } ∈ N $\xi =\lbrace \xi _n\rbrace _{n\in \mathbb {N}}$ a Hilbert space ( H , ⟨ · ⟩ ) $(\mathcal {H},\langle \cdot ,\cdot \rangle )$ the operator T $T_\xi$ is defined as associated to sesquilinear form Ω f g ∑ $\Omega _\xi (f,g)=\sum {N}} \langle _n\rangle _n g\rangle$ for h : | 2 < ∞ $f,g\in \lbrace h\in \mathcal {H}: \sum {N}}|\langle |^2<\infty ...

Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame can be regarded as a frame-like collection of subspaces in a Hilbert Communicated by Qiyu Sun. P.G.C. and A.H. were supported by NSF DMS 0704216. G.K. would like to thank the Department of Statistics at Stanford University and the Mathematics Depar...

$K$-frames as a generalization of frames were introduced by L. Gu{a}vruc{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new ge...

in this paper we introduce two-wavelet constants for square integrable representations of homogeneous spaces. we establishthe orthogonality relations for square integrable representationsof homogeneous spaces which give rise to the existence of aunique self adjoint positive operator on the set of admissiblewavelets. finally, we show that this operator is a constant multiple of identity operator...

We consider the bilinear Fourier integral operatorS(f, g)(x) =ZRdZRdei1(x,)ei2(x,)(x, , ) ˆ f()ˆg()d d,on modulation spaces. Our aim is to indicate this operator is well defined onS(Rd) and shall show the relationship between the bilinear operator and BFIO onmodulation spaces.