In this paper, we introduce the concept of dual frame of g-p-frame, and give the sufficient condition for a g-p-frame to have dual frames. Using operator theory and methods of functional analysis, we get some new properties of g-p-frame. In addition, we also characterize g-p-frame and g-q-Riesz bases by using analysis operator of g-p-Bessel sequence. c ©2017 All rights reserved.

In this paper, we show that in each nite dimensional Hilbert space, a frame of subspaces is an ultra Bessel sequence of subspaces. We also show that every frame of subspaces in a nite dimensional Hilbert space has frameness bound.

in this paper, we show that in each nite dimensional hilbert space, a frame of subspaces is an ultra bessel sequence of subspaces. we also show that every frame of subspaces in a nite dimensional hilbert space has frameness bound.

In this article, we show that a finite dimensional Hilbert space can have an infinite Bessel sequence, but a normalized Bessel sequence in a finite dimensional Hilbert space must be of finite length. A relation between the dimension of a given finite dimensional Hilbert space and the bound of any finite normalized tight frame for the underlying space is obtained. Also some properties of the fra...

A fifth-order CMOS continuous-time Bessel filter with a tunable 6to IS-MHZ cutoff frequency is described. This fully balanced transconductance-capacitor (G~ – C) leapfrog filter achieves a dynamic range of 55 dB while dissipating 96 mW in a 5-V 0.9-pm CMOS process. The on-chip master–slave tuning system uses a voltage-controlled oscillator (VCO).

In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new denition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we dene the fusion biorthogonal sequence, Bessel fusion basis, Hil...

Let H be a finite dimensional (real or complex) Hilbert space and let {ai}i=1 be a non-increasing sequence of positive numbers. Given a finite sequence of vectors F = {fi}pi=1 in H we find necessary and sufficient conditions for the existence of r ∈ N∪{∞} and a Bessel sequence G = {gi}i=1 in H such that F ∪ G is a tight frame for H and ‖gi‖ = ai for 1 ≤ i ≤ r. Moreover, in this case we compute ...

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- ...

we define a new function-valued inner product on l2(g), called ?-bracket product, where g is a locally compact abelian group and ? is a topological isomorphism on g. we investigate the notion of ?-orthogonality, bessel's inequality and ?-orthonormal bases with respect to this inner product on l2(g).

In this paper we study the Feichtinger Conjecture in frame theory, which was recently shown to be equivalent to the 1959 Kadison-Singer Problem in C-Algebras. We will show that every bounded Bessel sequence can be decomposed into two subsets each of which is an arbitrarily small perturbation of a sequence with a finite orthogonal decomposition. This construction is then used to answer two open ...