Related papers: On Gabor frames generated by sign-changing windows…
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…
We establish the restricted isometry property for finite dimensional Gabor systems, that is, for families of time--frequency shifts of a randomly chosen window function. We show that the $s$-th order restricted isometry constant of the…
We analyze the interplay between contact geometry and Gabor filters signal analysis in geometric models of the primary visual cortex. We show in particular that a specific framed lattice and an associated Gabor system is determined by the…
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…
The quantum mechanical harmonic oscillator Hamiltonian generates a one-parameter unitary group W(\theta) in L^2(R) which rotates the time-frequency plane. In particular, W(\pi/2) is the Fourier transform. When W(\theta) is applied to any…
This paper is concerned with two themes: imprisoned curves and the b-length functional. In an earlier paper by the author, it was claimed that an endless incomplete curve partially imprisoned in a compact set admits an endless null geodesic…
The theory of Gabor frames of functions defined on finite abelian groups was initially developed in order to better understand the properties of Gabor frames of functions defined over the reals. However, during the last twenty years the…
We present a method for constructing all bounded rational motions that frame a space curve $\mathbf{r}(t)$. This means that the motion guides an orthogonal frame along the curve such that one frame axis is in direction of the curve tangent.…
In a previous paper, the first two named authors established an isomorphism between the moduli space of framed flags of sheaves on the projective plane and the moduli space of stable representations of a certain quiver. In the present note,…
Our objective is to illuminate the global structure of non-orientable manifolds with signature-changing metrics, with particular emphasis on global topological obstructions. Using explicit geometric constructions based on the topology of…
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…
We investigate vector-valued Gabor frames (sometimes called Gabor superframes) based on Hermite functions $H_n$. Let $h= (H_0, H_1, ..., H_n)$ be the vector of the first $n+1$ Hermite functions. We give a complete characterization of all…
A frame is a system of vectors $S$ in Hilbert space $\mathscr{H}$ with properties which allow one to write algorithms for the two operations, analysis and synthesis, relative to $S$, for all vectors in $\mathscr{H}$; expressed in…
We investigate the reproducing properties of Gabor systems within the context of expansible groups. These properties are established in terms of density conditions. The concept of density that we employ mirrors the well-known Beurling…
The frame set conjecture for Hermite functions formulated in [Gr\"ochenig, J. Fourier Anal. Appl., 20(4):865-895, 2014] states that the Gabor frame set for these generators is the largest possible, that is, the time-frequency shifts of the…
The paper presents a survey over frame multipliers and related concepts. In particular, it includes a short motivation of why multipliers are of interest to consider, a review as well as extension of recent results, devoted to the…
Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply…
We show that every rationally sampled dilation-and-modulation system is unitarily equivalent with a multi-window Gabor system. As a consequence, frame theoretical results from Gabor analysis can be directly transferred to…
We interpret the Hilbert entropy of a convex projective structure on a closed higher-genus surface as the Hausdorff dimension of the non-differentiability points of the limit set in the full flag space $\mathcal F(\mathbb R^3)$.…
We prove uniform boundedness of certain boundary representations on appropriate fractional Sobolev spaces $W^{s,p}$ with $p>1$ for arbitrary Gromov hyperbolic groups. These are closed subspaces of $L^p$ and in particular Hilbert spaces in…