Related papers: On weaving g-frames for Hilbert spaces

We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…

We refute the widely held belief that the quantum weak value necessarily pertains to weak measurements. To accomplish this, we use the transverse position of a beam as the detector for the conditioned von Neumann measurement of a system…

Tight wavelet frames are computationally and theoretically attractive, but most existing multivariate constructions have various drawbacks, including low vanishing moments for the wavelets, or a large number of wavelet masks. We further…

One approach to ease the construction of frames is to first construct local components and then build a global frame from these. In this paper we will show that the study of the relation between a frame and its local components leads to the…

In this work, we consider some relationships between a closed range operator $T$ and a fusion frame $\mathcal{W}=(W_i,w_i)_{i\in I}$ for a Hilbert space $\mathcal{H}$ that provides that the sequence $(\overline{T(W_i)},v_i)_{i\in I}$ is a…

Dynamical sampling, as introduced by Aldroubi et al., deals with frame properties of sequences of the form $\{T^i f_1\}_{i\in \mathbb{N}}$, where $f_1$ belongs to Hilbert space $\h$ and $T:\h\rightarrow\h$ belongs to certain classes of the…

This paper shows that, when considering outdoor scenarios and wireless communications using the IEEE 802.11 protocol with dipole antennas, the ground reflection is a significant propagation mechanism. This way, the Two-Ray model for this…

Frames for operators or k-frames were recently considered by Gavruta (2012) in connection with atomic systems. Also generalized frames are important frames in the Hilbert space of bounded linear operators. Fusion frames, which are a special…

Accurately rendering the appearance of fabrics is challenging, due to their complex 3D microstructures and specialized optical properties. If we model the geometry and optics of fabrics down to the fiber level, we can achieve unprecedented…

Gravitational-wave astronomy of compact binaries relies on theoretical models of the gravitational-wave signal that is emitted as binaries coalesce. These models do not only need to be accurate, they also have to be fast to evaluate in…

In this papers we investigate the g-frame and Bessel g-sequence related to a linear bounded operator $K$ in Hilbert $C^{\ast}$-module and we establish some results.

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 definition of fusion dual sequence associated with a fusion…

Let $q\geq 2$ be an integer, and $\Bbb F_q^d$, $d\geq 1$, be the vector space over the cyclic space $\Bbb F_q$. The purpose of this paper is two-fold. First, we obtain sufficient conditions on $E \subset \Bbb F_q^d$ such that the inverse…

K-frames, a new generalization of frames, were recently considered by L. Gavruta in connection with atomic systems and some problems arising in sampling theory. Also, fusion frames are an important generalization of frames, applied in a…

We propose a graph-based process calculus for modeling and reasoning about wireless networks with local broadcasts. Graphs are used at syntactical level to describe the topological structures of networks. This calculus is equipped with a…

In wireless communications, transforming network into graphs and processing them using deep learning models, such as Graph Neural Networks (GNNs), is one of the mainstream network optimization approaches. While effective, the generative AI…

Gating mechanisms have emerged as an effective strategy integrated into model designs beyond recurrent neural networks for addressing long-range dependency problems. In a broad understanding, it provides adaptive control over the…

We investigate the relevance of admissibility criteria based on Plancherel measure for the characterization of tight Weyl-Heisenberg frames with integer oversampling. For this purpose we observe that functions giving rise to such…

We analyze the notion of reproducing pair of weakly measurable functions, which generalizes that of continuous frame. We show, in particular, that each reproducing pair generates two Hilbert spaces, conjugate dual to each other. Several…

Latent variable models (LVMs) learn probabilistic models of data manifolds lying in an \emph{ambient} Euclidean space. In a number of applications, a priori known spatial constraints can shrink the ambient space into a considerably smaller…