This paper is devoted to an approximation problem for operators in Hilbert space, that appears when one tries to study geometrically the cascade algorithm in wavelet theory. Let H be a Hilbert space, and let π be a representation of L∞ (T) on H. Let R be a positive operator in L∞ (T) such that R (11) = 11, where 11 denotes the constant function 1. We study operators M on H (bounded, but noncont...

in this paper we get some results and applications for duals and approximate duals of g-frames in hilbert spaces. in particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of hilbert spaces. we also obtain some results for perturbations of approximate duals.

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.

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...

The Fourier transform (FT) nicely represents a wiggling, sinelike data set with only a few peaks in the frequency domain. But while the FT is appropriate for simple stationary data like harmonic waves, complicated signals or images require more elaborate transforms. These transforms must catch fast local variations, detect blurred object contours, differentiate textures, and capture different s...

In this paper, we propose the Fourier frequency vector (FFV), inherently, associated with multidimensional Fourier transform. With the help of FFV, we are able to provide physical meaning of so called negative frequencies in multidimensional Fourier transform (MDFT), which in turn provide multidimensional spatial and space-time series analysis. The complex exponential representation of sinusoid...

We describe three methods to determine the structure of (sufficiently continuous) representations of the algebra Ba(E) of all adjointable operators on a Hilbert B–module E by operators on a Hilbert C–module. While the last and latest proof is simple and direct and new even for normal representations of B(H) (H some Hilbert space), the other ones are direct generalizations of the representation ...

Suppose that G is a locally compact group and U is a representation of a closed subgroup H of G on a Hilbert space H. We use nonabelian duality for crossed products of C∗-algebras to study the following problem: when does U extend to a representation of G on the same space H?

In this paper, we present a practical application of non-linear system identification, namely to a mechanical system with a backlash component, based on the skeleton curve reconstruction technique. In the case presented, the identification procedure employs the instantaneous amplitude and frequency of the input and the output of the base motion system under certain forced excitation. Hilbert tr...