A probabilistic frame is a Borel probability measure with finite second moment whose support spans R. A Parseval probabilistic frame is one for which the associated matrix of second moment is the identity matrix in R. Each probabilistic frame is canonically associated to a Parseval probabilistic frame. In this paper, we show that this canonical Parseval probabilistic frame is the closest Parsev...

We investigate frame theory over the binary field Z2, following work of Bodmann, Le, Reza, Tobi and Tomforde. We consider general finite dimensional vector spaces V over Z2 equipped with an (indefinite) inner product (·, ·)V which can be an arbitrary bilinear functional. We characterize precisely when two such spaces (V, (·, ·)V ) and (W, (·, ·)W ) are unitarily equivalent in the sense that the...

G-frames are natural generalizations of frames which provide more choices on analyzing functions from frame expansion coefficients. First, they were defined in Hilbert spaces and then generalized on C*-Hilbert modules. In this paper, we first generalize the concept of g-frames to Hilbert modules over pro-C*-algebras. Then, we introduce the g-frame operators in such spaces and show that they sha...

We consider classes of reconstruction systems (RS’s) for finite dimensional real or complex Hilbert spaces H, called group reconstruction systems (GRS’s), that are associated with representations of finite groups G. These GRS’s generalize frames with high degree of symmetry, such as harmonic or geometrically uniform ones. Their canonical dual and canonical Parseval are shown to be GRS’s. We est...

The excess of a sequence in a Hilbert space H is the greatest number of elements that can be removed yet leave a set with the same closed span. This paper proves that if F is a frame for H and there exist infinitely many elements gn ∈ F such that F \ {gn} is complete for each individual n and if there is a uniform lower frame bound L for each frame F \ {gn}, then for each ε > 0 there exists an ...

In this paper we present a constructive proof that the set of Gabor frames is pathconnected in the L2(Rn)-norm. In particular, this result holds for the set of Gabor Parseval frames as well as for the set of Gabor orthonormal bases. In order to prove this result, we introduce a construction which shows exactly how to modify a Gabor frame or Parseval frame to obtain a new one with the same prope...

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.

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- ...

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