Related papers: Discrete Quaternionic (Multi-window) Gabor Systems
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
We introduce the notion of a generalized fusion frame in quaternionic Hilbert space. A characterization of generalized fusion frame in quaternionic Hilbert space with the help of frame operator is being discussed. Finally, we construct…
In this paper, we investigate extreme singular values of the analysis matrix of a Gabor frame $(g, \Lambda)$ with a random window $g$. Columns of such matrices are time and frequency shifts of $g$, and $\Lambda\subset…
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…
This is the first in a series of papers in which we describe explicit structural properties of spaces of diagonal rectangular harmonic polynomials in $k$ sets of $n$ variables, both as $GL_k$-modules and $S_n$-modules, as well as some of…
In this paper we construct frames of Gabor type for the space $L^2_{rad}(\R^d)$ of radial $L^2$-functions, and more generally, for subspaces of modulation spaces consisting of radial distributions. Hereby, each frame element itself is a…
We propose a model describing the scattering of hadrons as bound states of their constituent quarks. We analyze the role of simultaneity in measurements of the characteristics of different particles for the description of relativistic…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
We obtain Gabor frame characterisations of modulation spaces defined via a class of translation-modulation invariant Banach spaces of distributions that was recently introduced in $[10]$. We show that these spaces admit an atomic…
We study the structure of a Leibniz triple system $\mathcal{E}$ graded by an arbitrary abelian group $G$ which is considered of arbitrary dimension and over an arbitrary base field $\mathbb{K}$. We show that $\mathcal{E}$ is of the form…
The objective of this work is to examine the integrability of Hamiltonian systems in $2D$ spaces with variable curvature of certain types. Based on the differential Galois theory, we announce the necessary conditions of the integrability.…
Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and…
We construct a set of quaternionic metamonogenic functions (that is, in $\mbox{Ker}(D+\lambda)$ for diverse $\lambda$) in the unit disk, such that every metamonogenic function is approximable in the quaternionic Hilbert module $L^2$ of the…
In this work we derive a simple argument which shows that Gabor systems consisting of odd functions of $d$ variables and symplectic lattices of density $2^d$ cannot constitute a Gabor frame. In the 1--dimensional, separable case, this is a…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
We consider $\G$-graded commutative algebras, where $\G$ is an abelian group. Starting from a remarkable example of the classical algebra of quaternions and, more generally, an arbitrary Clifford algebra, we develop a general viewpoint on…
We study the existence of Gabor orthonormal bases with window the characteristic function of the set W=[0,a] U [b+a, b+1] of measure 1, with a, b>0. By the symmetries of the problem, we can restrict our attention to the case a<=1/2. We…
It is shown that physical signals and space-time intervals modeled on split-octonion geometry naturally exhibit properties from conventional (3+1)-theory (e.g. number of dimensions, existence of maximal velocities, Heisenberg uncertainty,…
We generalize three main concepts of Gabor analysis for lattices to the setting of model sets: Fundamental Identity of Gabor Analysis, Janssen's representation of the frame operator and Wexler-Raz biorthogonality relations. Utilizing the…
A proposal for the matrix model formulation of the M-theory on a space with a boundary is given. A general machinery for modding out a symmetry in M(atrix) theory is used for a Z_2 symmetry changing the sign of the X_1 coordinate. The…