Related papers: Uncertainty principles for the windowed offset lin…
Let $f$ be a finite signal. The classical uncertainty principle tells us that the product of the support of $f$ and the support of $\hat{f}$, the Fourier transform of $f$, must satisfy $|supp(f)|\cdot|supp(\hat{f})|\geq |G|$. Recently,…
For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent. Accordingly, the information-entropic formulation of the uncertainty principle becomes more appropriate than the…
The purpose of this short note is to exhibit a new connection between the Heisenberg Uncertainty Principle on the line and the Breitenberger Uncertainty Principle on the circle, by considering the commutator of the multiplication and…
Recently, universally valid uncertainty relations have been established to set a precision limit for any instruments given a disturbance constraint in a form more general than the one originally proposed by Heisenberg. One of them leads to…
In this paper, we generalise Hardy's uncertainty principle to vector-valued functions, and hence to operators. The principle for operators can be formulated loosely by saying that the kernel of an operator cannot be localised near the…
The role of the Uncertainty Principle is examined through the examples of squeezing, information capacity, and position monitoring. It is suggested that more attention should be directed to conceptual considerations in quantum information…
Quantum gravity models predict a minimal measurable length which gives rise to a modification in the uncertainty principle. One of the simplest manifestations of these generalised uncertainty principles is the linear quadratic generalised…
Although there are many mathematical theories to address uncertain phenomena however, these theories are presented under implicit presupposition that uncertainty of objects is accurately measurable while not considering that the measure of…
The underlying mathematics of the wavelet formalism is a representation of the inhomogeneous Lorentz group or the affine group. Within the framework of wavelets, it is possible to define the ``window'' which allows us to introduce a…
We prove the logarithmic convexity of certain quantities, which measure the quadratic exponential decay at infinity and within two characteristic hyperplanes of solutions of Schr\"odinger evolutions. As a consequence we obtain some…
We first present a generalization of the Robertson-Heisenberg uncertainty principle. This generalization applies to mixed states and contains a covariance term. For faithful states, we characterize when the uncertainty inequality is an…
Generalized Uncertainty Principle (GUP) was obtained in string theory and quantum gravity and suggested the existence of a fundamental minimal length which, as was established, can be obtained within the deformed Heisenberg algebra. We use…
The linear canonical transform (LCT) serves as a powerful generalization of the Fourier transform (FT), encapsulating various integral transforms within a unified framework. This versatility has made it a cornerstone in fields such as…
The sampling theorem for the offset linear canonical transform (OLCT) of bandlimited functions in polar coordinates is an important signal analysis tool in many fields of signal processing and medical imaging. This study investigates two…
Heisenberg's uncertainty principle states that the position and momentum of a particle cannot be sharply determined simultaneously. Standard-deviation and entropic formulations capture the spread of the probability distribution but say…
The general model of coagulation is considered. For basic classes of unbounded coagulation kernels the central limit theorem (CLT) is obtained for the fluctuations around the dynamic law of large numbers (LLN). A rather precise rate of…
Uncertainty principles for concentration of signals into truncated subspaces are considered. The ``classic'' uncertainty principle is explored as a special case of a more general operator framework. The time-bandwidth concentration problem…
In this paper, we study forms of the uncertainty principle suggested by problems in control theory. We obtain a version of the classical Paneah-Logvinenko-Sereda theorem for the annulus. More precisely, we show that a function with spectrum…
Hardy's uncertainty principle is a classical result in harmonic analysis, stating that a function in $L^2(\mathbb{R}^d)$ and its Fourier transform cannot both decay arbitrarily fast at infinity. In this paper, we extend this principle to…
The nonnegativity of the density operator of a state is faithfully coded in its Wigner distribution, and this places constraints on the moments of the Wigner distribution. These constraints are presented in a canonically invariant form…