Related papers: Gabor orthonormal bases generated by the unit cube…
In this expository note we present an introduction to the Gabor wave front set. As is often the case, this tool in microlocal analysis has been introduced and reinvented in different forms which turn out to be equivalent or intimately…
Let $\Lambda$ be a commutative Noetherian ring, and let $I$ be a proper ideal of $\Lambda$, $R=\Lambda /I$. Consider the polynomial rings $T=\Lambda [x_1,...x_n]$ and $A=R[x_1,...,x_n]$. Suppose that linear equations are solvable in…
We consider the notion of unitary transformations forming bases for subspaces of $M(d,\mathbb{C})$ such that the square of Hilbert-Schmidt inner product of matrices from the differing bases is a constant. Moving from the qubit case,…
In this paper we develop constructive invertibility conditions for the twisted convolution. Our approach is based on splitting the twisted convolution with rational parameters into a finite number of weighted convolutions, which can be…
We prove that the HRT conjecture holds when the Gabor system consists of a 4-point set in the time-frequency plane and a square-integrable function that is ultimately positive. We also prove the conjecture for Gabor systems generated by an…
We investigate the extrinsic geometry of causal sets in $(1+1)$-dimensional Minkowski spacetime. The properties of boundaries in an embedding space can be used not only to measure observables, but also to supplement the discrete action in…
Astronomical time series often have non-uniform sampling in time, or irregular cadences, with long gaps separating clusters of observations. Some of these data sets are also explicitly non-Gaussian with respect to the expected model fit, or…
Gabor analysis which can be traced back to Dennis Gabor's influential 1946 paper \emph{Theory of communication}, is concerned with both the theory and the applications of the approximation properties of sets of time and frequency shifts of…
We study bosonic systems on a spacetime lattice defined by path integrals of commuting fields. We introduce branch-independent bosonic (BIB) systems, whose path integral is independent of the branch structure of the spacetime simplicial…
Nonstationary Gabor frames, recently introduced in adaptive signal analysis, represent a natural generalization of classical Gabor frames by allowing for adaptivity of windows and lattice in either time or frequency. Due to the lack of a…
We establish a necessary density criterion for the identifiability of time-frequency structured classes of Hilbert-Schmidt operators. The density condition is based on the density criterion for Gabor frames and Riesz bases in the space of…
The Talbot effect -- a near-field diffraction phenomenon in which a periodic wavefront self-images at regular distances -- can be transposed to the time--frequency domain via the space--time duality between diffraction and dispersive…
Observables in a quantum system, represented by a Hilbert space, are given by the orthogonal bases of the aforementioned Hilbert space. Categorical Quantum Mechanics provides further abstraction of such observables, allowing for a…
The upside-down simple harmonic oscillator system is studied in the contexts of quantum mechanics and classical statistical mechanics. It is shown that in order to study in a simple manner the creation and decay of a physical system by ways…
Parametrized and random unitary (or orthogonal) $n$-qubit circuits play a central role in quantum information. As such, one could naturally assume that circuits implementing symplectic transformations would attract similar attention.…
Shapere and Wilczek ( Phys. Rev. Lett. 109, 160402 and 200402 (2012)) have recently described certain singular Lagrangian systems which display spontaneous breaking of time translation symmetry. We begin by considering the standard Lienard…
We derive the approximate analytical solutions of the bound timelike geodesic orbits in the effective-one-body (EOB) frame with extreme-mass ratio limit. The analytical solutions are expressed in terms of the elliptic integrals using Mino…
Scalar wave scattering by many small particles of arbitrary shapes with impedance boundary condition is studied. The problem is solved asymptotically and numerically under the assumptions a << d << lambda, where k = 2pi/lambda is the wave…
Gauging introduces gauge fields in order to localize an existing global symmetry, resulting in a dual global symmetry on the gauge fields that can be gauged again. By iterating the gauging process on spin chains with Abelian group…
Suppose $\Lambda \subseteq \RR^2$ has the property that any two exponentials with frequency from $\Lambda$ are orthogonal in the space $L^2(D)$, where $D \subseteq \RR^2$ is the unit disk. Such sets $\Lambda$ are known to be finite but it…