In this paper, we first discuss about canonical dual of g<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font...

Consider a continuous function g ∈ L2(R) that is supported on [−1, 1] and generates a Gabor frame with translation parameter 1 and modulation parameter 0 < b < 2N 2N+1 for some N ∈ N. Under an extra condition on the zeroset of the window g we show that there exists a continuous dual window supported on [−N, N]. We also show that this result is optimal: indeed, if b > 2N 2N+1 then a dual window ...

Qualitative Process theory provides a formal representation for human-like models of continuous processes. However, qualitative reasoning systems frequently rely on hand-made models which inhibits expansion into new domains. A representation that unifies QP theory with natural language expressions would allow these systems to expand their models by reading and interaction, thus greatly increasi...

‎In this paper‎, ‎first we develop the duality concept for $g$-Bessel sequences‎ ‎and Bessel fusion sequences in Hilbert spaces‎. ‎We obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎We also expand every $g$-Bessel ‎sequence to a frame by summing some elements‎. ‎We define the restricted isometry property for ‎$g$-frames and generalize some resu...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We study the frame $mathfrak{O}(Min(mathcal{R}L))$ of minimal prime ideals of $mathcal{R}L$ in relation to $beta L$. For $Iinbeta L$, denote by $textit{textbf{O}}^I$ the ideal ${alphainmathcal{R}Lmidcozalphain I}$ of $mathcal{R}L$. We show that sending $I$ to the set of minimal prime ...

In this paper, we introduce the concepts of $ast$-K-g-Frames in Hilbert $mathcal{A}$-modules and we establish some results.

in this paper, we define and study the notion of the real-valued functions on a frame $l$. we show that $f(l) $, consisting of all frame homomorphisms from the power set of $mathbb{r}$ to a frame $ l$, is an $f$-ring, as a generalization of all functions from a set $x$ into $mathbb r$. also, we show that $f(l) $ is isomorphic to a sub-$f$-ring of $mathcal{r}(l)$, the ring of real-valued continu...

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 ...