相关论文: Weighted Fusion Frame Construction via Spectral Te…

A framework is a graph and a map from its vertices to R^d. A framework is called universally rigid if there is no other framework with the same graph and edge lengths in R^d' for any d'. A framework attachment is a framework constructed by…

We introduce a formalism for handling general spaces of hierarchical tilings, a category that includes substitution tilings, Bratteli-Vershik systems, S-adic transformations, and multi-dimensional cut-and-stack transformations. We explore…

Equiangular tight frames (ETFs) and biangular tight frames (BTFs) - sets of unit vectors with basis-like properties whose pairwise absolute inner products admit exactly one or two values, respectively - are useful for many applications. A…

Video Frame Interpolation synthesizes non-existent images between adjacent frames, with the aim of providing a smooth and consistent visual experience. Two approaches for solving this challenging task are optical flow based and kernel-based…

Let $\mathcal{H}$ be a (separable) Hilbert space and $\{e_k\}_{k\geq 1}$ a fixed orthonormal basis of $\mathcal{H}$. Motivated by many papers on scaled projections, angles of subspaces and oblique projections, we define and study the notion…

Modern and future high precision pointing space missions face increasingly high challenges related to the widespread use of large flexible structures. The development of new modeling tools which are able to account for the multidisciplinary…

An introductory theory of frames on finite dimensional quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.

Finite frame theory has become a powerful tool for many applications of mathematics. In this paper we introduce a new area of research in frame theory: Integer frames. These are frames having all integer coordinates with respect to a fixed…

In vertex algebra theory, fusion rules are described as the dimension of the vector space of intertwining operators between three irreducible modules. We describe fusion rules in the category of weight modules for the Weyl vertex algebra.…

Construction of Symmetric Complex Tight wavelet Frames from Pseudo Splines via Matrix Extension with Symmetry.

Configurations of subspaces like equichordal and equiisoclinic tight fusion frames, which are in some sense optimally spread apart and which also have reconstruction properties emulating those of orthonormal bases, are useful in various…

Frames in separable Hilbert spaces gives stable analysis and reconstruction of each vector in the underlying space. In this paper, we study frame conditions for a collection of matrix-valued functions obtained by non-uniform shifts. We give…

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…

In this present paper we introduce weaving Hilbert space frames in the continuous case, we give new approaches for manufacturing pairs of woven continuous frames and we obtain new properties in continuous weaving frame theory related to…

Controlled frames which presented to improve the numerical output of iterative algorithms for inverting the frame operator, have been introduced by Balazs and et al. Also, these frames are used by Bogdanova and et al. for spherical…

A frame is a generalization of a basis of a vector space to a redundant overspanning set whose vectors are linearly dependent. Frames find applications in signal processing and quantum information theory. We present a genetic algorithm that…

For applications like the numerical solution of physical equations a discretization scheme for operators is necessary. Recently frames have been used for such an operator representation. In this paper, we apply fusion frames for this task.…

We consider frames in a finite-dimensional Hilbert space Hn where frames are exactly the spanning sets of the vector space. We present a method to determine the maximum robustness of a frame. We present results on tight subframes and…

A solid slender beam of length $L$, made from a material of Young's modulus $Y$ and subject to a gentle compressive force $F$, requires a volume of material proportional to $L^{3}f^{1/2}$ [where $f\equiv F/(YL^{2})\ll 1$] in order to be…

We consider the notion of finite dimensional reconstructions systems (RS's), which includes the fusion frames as projective RS's. We study erasures, some geometrical properties of these spaces, the spectral picture of the set of all dual…