Related papers: Discrete Quaternionic (Multi-window) Gabor Systems
We consider the following problem: given a set $\Lambda \subset \mathbb{R} \times \mathbb{R}$ and $p \neq 2$, does there exist a function $g \in L^p(\mathbb{R})$ such that the Gabor system $\{g(x-t) e^{2 \pi isx}\}$, $(t,s) \in \Lambda$,…
We introduce new frames, called \textit{metaplectic Gabor frames}, as natural generalizations of Gabor frames in the framework of metaplectic Wigner distributions. Namely, we develop the theory of metaplectic atoms in a full-general setting…
The main purpose of the paper is to give a characterization of all compactly supported dual windows of a Gabor frame. As an application, we consider an iterative procedure for approximation of the canonical dual window via compactly…
We introduce new classes of right quaternionic Hilbert spaces of Bargmann-Fock type $\mathcal{GB}_{m}^{2}(\mathbb{H})$, labeled by nonnegative integer $m$, generalizing the so-called slice hyperholomorphic Bargmann-Fock space introduced…
In the present investigation we are linking noncommutative geometry over noncommutative tori with Gabor analysis, where the first has its roots in operator algebras and the second in time-frequency analysis. Therefore we are in the position…
We investigate the conformal window of four-dimensional gauge theories with fermionic matter fields in multiple representations. Of particularly relevant examples are the ultra-violet complete models with fermions in two distinct…
In a recent paper in Appl. Comput. Harmon. Anal. 38(2), 196--221 (2014) we have introduced and studied the notion of weak Hamiltonian deformation of a Gabor (=Weyl-Heisenberg) frame. In this Note we use these results to prove that one can…
This is a rough transcript of talks given at the Workshop on Groups & Algebras in M Theory at Rutgers University, May 31--Jun 04, 2005. We review the basic motivation for a pre-geometric formulation of nonperturbative String/M theory, and…
Redundancy is the qualitative property which makes Hilbert space frames so useful in practice. However, developing a meaningful quantitative notion of redundancy for infinite frames has proven elusive. Though quantitative candidates for…
A Wilson system is a collection of finite linear combinations of time frequency shifts of a square integrable function. In this paper we use the fact that a Wilson system is a shift-invariant system to explore its relationship with Gabor…
In this article we discuss the interaction between the geometry of a quaternion-Kahler manifold M and that of the Grassmannian G(3,g) of oriented 3-dimensional subspaces of a compact Lie algebra g. This interplay is described mainly through…
Shifted and modulated Gaussian functions play a vital role in the representation of signals. We extend the theory into a quaternionic setting, using two exponential kernels with two complex numbers. As a final result, we show that every…
For a class of compactly supported windows we characterize the frame property for a Gabor system $\mts,$ for translation parameters $a$ belonging to a certain range depending on the support size. We show that the obstructions to the frame…
In this paper we study the structure of the Hilbert space for the recent noncommutative geometry models of gauge theories. We point out the presence of unphysical degrees of freedom similar to the ones appearing in lattice gauge theories…
The author studies the structure of space $ \mathbf {L} _ {2} (G) $ of vector-valued functions that are square integrable in a bounded connected domain $ G $ of the three-dimensional space with a smooth boundary and the role of gradient…
Suppose that $G$ is a simple adjoint reductive group over $\mathbf{Q}$, with an exceptional Dynkin type, and with $G(\mathbf{R})$ quaternionic (in the sense of Gross-Wallach). Then there is a notion of modular forms for $G$, anchored on the…
It is known that, in general, an affine or Gabor AP-frame is an $L^2(\mathbb{R})$-frame and conversely. In part as a consequence of the Ergodic Theorem, we prove a necessary and sufficient condition for an affine (wavelet) system…
We discuss the relationship between quaternion algebras and quadratic forms with a focus on computational aspects. Our basic motivating problem is to determine if a given algebra of rank 4 over a commutative ring R embeds in the 2x2-matrix…
We investigate systems of the form $\{A^tg:g\in\mathcal{G},t\in[0,L]\}$ where $A \in B(\mathcal{H})$ is a normal operator in a separable Hilbert space $\mathcal{H}$, $\mathcal{G}\subset \mathcal{H}$ is a countable set, and $L$ is a positive…
For two given full-rank lattices $\mathcal{L}=A\mathbb{Z}^d$ and $\mathcal{K}=B\mathbb{Z}^d$ in $\mathbf{R}^d$, where $A$ and $B$ are nonsingular real $d\times d$ matrices, a function $g(\bf{t})\in L^2(\mathbf{R}^d)$ is called a Parseval…