Related papers: More Uncertainty Principles for Metaplectic Time-F…
Space-time varying media enable unprecedented control over electromagnetic waves, yet most existing studies assume idealized, nondispersive materials and thus fail to capture the intrinsic frequency dispersion of realistic platforms. Here,…
Better knowing the precision on the measured value of the Brillouin peak frequencies is essen-tial in order to use it to deduce parameters related to studied materials. Modern methods for evaluating uncertainties are based on the…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
In this paper, we study a few versions of the uncertainty principle for the windowed Opdam--Cherednik transform. In particular, we establish the uncertainty principle for orthonormal sequences, Donoho--Stark's uncertainty principle,…
The aim of this paper is to establish a few qualitative uncertainty principles for the windowed Opdam-Cherednik transform on weighted modulation spaces associated with this transform. In particular, we obtain the Cowling-Price's, Hardy's…
Time averaging of weak values using the quantum transition path time probability distribution enables us to establish a general uncertainty principle for the weak values of two not necessarily Hermitian operators. This new principle is a…
The uncertainty principle constitutes one of the famous physical concepts which continues to attract researchers from different related fields since its discovery due to its utility in many applications. Among the classical (Fourier-based)…
We formulate and prove an analogue of Beurling's theorem for the Fourier transform on the Heisenberg group. As a consequence we deduce Hardy and Cowling-Price theorems.
We study the short-time Fourier transform on the space $\mathcal{K}_{1}'(\mathbb{R}^n)$ of distributions of exponential type. We give characterizations of $\mathcal{K}_{1}'(\mathbb{R}^n)$ and some of its subspaces in terms of modulation…
Many stochastic processes are defined on special geometrical objects like spheres and cones. We describe how tools from harmonic analysis, i.e. Fourier analysis on groups, can be used to investigate probability density functions (pdfs) on…
In this paper we generalize the continuous quaternion windowed Fourier transform called the multivariate two sided continuous quaternion windowed Fourier transform. Using the two sided quaternion Fourier transform we derive several…
In this paper, we have given a new definition of continuous fractional wavelet transform in $\mathbb{R}^N$, namely the multidimensional fractional wavelet transform (MFrWT) and studied some of the basic properties along with the inner…
In this paper we derive a Heisenberg-type uncertainty principle for the continuous Clifford wavelet transform. A brief review of Clifford algebra/analysis, wavelet transform on $\mathbb{R}$ and Clifford-Fourier transform and their…
Reliable models of the thermodynamic properties of materials are critical for industrially relevant applications that require a good understanding of equilibrium phase diagrams, thermal and chemical transport, and microstructure evolution.…
In this note we provide a negative answer to a question raised by M. Kreisel concerning a condition on the short-time Fourier transform that would imply the HRT conjecture. In particular we provide a new type of uncertainty principle for…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
A method is described for predicting statistical properties of turbulence. Collections of Fourier amplitudes are represented by nonuniformly spaced modes with enhanced coupling coefficients. The statistics of the full dynamics can be…
We develop a convergent variational perturbation theory for the frequency of time-periodic solutions of nonlinear dynamical systems. The power of the theory is illustrated by applying it to the Duffing oscillator.
We present a reduced basis technique for long-time integration of parametrized incompressible turbulent flows. The new contributions are threefold. First, we propose a constrained Galerkin formulation that corrects the standard Galerkin…
In digital signal processing time-frequency transforms are used to analyze time-varying signals with respect to their spectral contents over time. Apart from the commonly used short-time Fourier transform, other methods exist in literature,…