相关论文: Density, Overcompleteness, and Localization of Fra…

Computing the excess as a method of measuring the redundancy of frames was recently introduced to address certain issues in frame theory. In this paper, the concept of excess for fusion frames is studied. Then, several explicit methods are…

We study spanning properties of a family of functions translated along simple model sets. We characterize tight frame and dual frame generators for such irregular translates and we apply the results to Gabor systems. We use the connection…

Answering a question of Lindholm, we prove strict density inequalities for sampling and interpolation in Fock spaces of entire functions in several complex variables defined by a plurisubharmonic weight. In particular, these spaces do not…

The densities of small linear structures (such as arithmetic progressions) in subsets of Abelian groups can be expressed as certain analytic averages involving linear forms. Higher-order Fourier analysis examines such averages by…

We derive necessary conditions for localization of continuous frames in terms of generalized Beurling densities. As an important application we provide necessary density conditions for sampling and interpolation in a very large class of…

The theory of descriptive nearness is usually adopted when dealing with sets that share some common properties even when the sets are not spatially close, i.e., the sets have no members in common. Set description results from the use of…

Decomposition spaces are a class of function spaces constructed out of well-behaved coverings and partitions of unity of a set. The structure of the covering of the set determines the properties of the decomposition space. Besov spaces,…

Was paper 839 in the author's list until winter 2023 when it was divided into three. Part I: We would like to generalize imaginary elements, weight of ortp$(a,M,N), {\mathbf P}$-weight, ${\mathbf P}$-simple types, etc. from [She90, Ch.…

Category-level object pose estimation aims to predict the pose and size of arbitrary objects in specific categories. Existing methods struggle with the inherent incompleteness of observed point clouds, which limits their ability to capture…

Re-localizing a camera from a single image in a previously mapped area is vital for many computer vision applications in robotics and augmented/virtual reality. In this work, we address the problem of estimating the 6 DoF camera pose…

We show that for algebraic groups over local fields of characteristic zero, the following are equivalent: Every homomorphism has a closed image, every unitary representation decomposes into a direct sum of finite-dimensional and mixing…

For a given class ${\cal F}$ of uniform frames of fixed redundancy we define a Grassmannian frame as one that minimizes the maximal correlation $|< f_k,f_l >|$ among all frames $\{f_k\}_{k \in {\cal I}} \in {\cal F}$. We first analyze…

Fusion frames are a convenient tool in applications where we deal with a large amount of data or when a combination of local data is needed. Oblique dual fusion frames are suitable in situations where the analysis for the data and its…

Approximately dual frames as a generalization of duality notion in Hilbert spaces have applications in Gabor systems, wavelets, coorbit theory and sensor modeling. In recent years, the computing of the associated deviations of the canonical…

Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…

This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…

Let $\mathcal F_0=\{f_i\}_{i\in\mathbb{I}_{n_0}}$ be a finite sequence of vectors in $\mathbb C^d$ and let $\mathbf{a}=(a_i)_{i\in\mathbb{I}_k}$ be a finite sequence of positive numbers. We consider the completions of $\cal F_0$ of the form…

In many applications, we desire neural networks to exhibit invariance or equivariance to certain groups due to symmetries inherent in the data. Recently, frame-averaging methods emerged to be a unified framework for attaining symmetries…

This survey offers a systematic and streamlined exposition of the most important characterizations of Gabor frames over a lattice. The goal is to collect the most important characterizations of Gabor frames and offer a systematic exposition…

With a simple generic approach, we develop a classification that encodes and measures the strength of completeness (or compactness) properties in various types of spaces and ordered structures. The approach also allows us to encode notions…