Related papers: Time-Frequency Localization Operators and a Berezi…
We initiate the study of weighted multi-Toeplitz operators associated with noncommutative regular domains in B(H)^n. These operators are acting on the full Fock space with n generators and have as symbols free pluriharmonic functions.…
Control design for linear, time-invariant mechanical systems typically requires an accurate low-order approximation in the low frequency range. For example a series expansion of the transfer function around zero consisting of a mass,…
Using the methods of ordinary quantum mechanics we study $\kappa$-Minkowski space as a quantum space described by noncommuting self-adjoint operators, following and enlarging arXiv:1811.08409. We see how the role of Fourier transforms is…
Motivated by applications to signal processing and mathematical physics, recent work on the concept of time-varying bandwidth has produced a class of function spaces which generalize the Paley-Wiener spaces of bandlimited functions: any…
In orthogonal time frequency space (OTFS) modulation, information-carrying symbols reside in the delay-Doppler (DD) domain. By operating in the DD domain, an appealing property for communication arises: time-frequency (TF) dispersive…
We present a new approach for constructing optical phase-space-time-frequency tomography (OPSTFT) of an optical wave field. This tomography can be measured by using a novel four-window optical imaging system based on two local oscillator…
Time-frequency transforms represent a signal as a mixture of its time domain representation and its frequency domain representation. We present efficient algorithms for the quantum Zak transform and quantum Weyl-Heisenberg transform.
Wave equations are fundamental to describing a vast array of physical phenomena, yet their simulation in inhomogeneous media poses a computational challenge due to the highly oscillatory nature of the solutions. To overcome the high costs…
This work considers uncertainty relations on time frequency distributions from a signal processing viewpoint. An uncertainty relation on the marginalizable time frequency distributions is given. A result from quantum mechanics is used on…
We study decay and smoothness properties for eigenfunctions of compact localization operators. Operators with symbols a in the wide modulation space M^{p,\infty} (containing the Lebesgue space L^p), p<\infty, and windows \f_1,\f_2 in the…
This article is a review on Berezin-Toeplitz operator and Berezin-Toeplitz deformation quantization for compact quantizable Kaehler manifolds. The basic objects, concepts, and results are given. This concerns the correct semi-classical…
We study localization effects of disorder on the spectral and dynamical properties of Schroedinger operators with random potentials. The new results include exponentially decaying bounds on the transition amplitude and related projection…
In this paper we construct directionally sensitive functions that can be viewed as directional time-frequency representations. We call such a sequence a rotational uniform covering frame and by studying rotations of the frame, we derive the…
This paper concerns dual frames multipliers, i.e. operators in Hilbert spaces consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames, respectively. The goal of the…
Graph signal processing deals with signals which are observed on an irregular graph domain. While many approaches have been developed in classical graph theory to cluster vertices and segment large graphs in a signal independent way, signal…
For $0<p\leq\infty$, let $F^{p}_\varphi$ be the Fock space induced by a weight function $\varphi$ satisfying $ dd^c \varphi \simeq \omega_0$. In this paper, given $p\in (0, 1]$ we introduce the concept of weakly localized operators on $…
We develop a transfer operator-based method for the detection of coherent structures and their associated lifespans. Characterising the lifespan of coherent structures allows us to identify dynamically meaningful time windows, which may be…
We introduce a new class of operators, called Berezin sectorial operators, which generalizes classical sectorial operators. We provide examples on the Hardy-Hilbert space showing that there exist operators that are Berezin sectorial but not…
In this article, we prove Herglotz's theorem for Hilbert-valued time series. This requires the notion of an operator-valued measure, which we shall make precise for our setting. Herglotz's theorem for functional time series allows to…
Surface water waves are considered propagating over highly variable non-smooth topographies. For this three dimensional problem a Dirichlet-to-Neumann (DtN) operator is constructed reducing the numerical modeling and evolution to the two…