Related papers: Uncertainty principles for the Opdam-Cherednik tra…
We consider the four dimensional Euclidean Maxwell theory with a Chern-Simons term on the boundary. The corresponding gauge invariant boundary conditions become dependent on tangential derivatives. Taking the four-sphere as a particular…
Some aspects of application of the Uncertainty Principle in the range of interaction radiation with matter surveyed. The procedure of adjustment is proposed at calculation of values of an electromagnetic energy in a quantum theory of a…
We study a variant of the uncertainty principle in terms of the annihilation and creation operator on generalized Segal Bargmann spaces, which are used for the FBI-Bargmann transform. In addition, we compute the Berezin transform of these…
In the present work the role that a generalized uncertainty principle could play in the quantization of the electromagnetic field is analyzed. It will be shown that we may speak of a Fock space, a result that implies that the concept of…
We obtain two-sided estimates for the heat kernel (or the fundamental function) associated with the following fractional Schr\"odinger operator with negative Hardy potential $$\Delta^{\alpha/2} -\lambda |x|^{-\alpha}$$ on $\RR^d$, where…
We prove a sharp version of the Hardy uncertainty principle for Schr\"odinger equations with external bounded electromagnetic potentials, based on logarithmic convexity properties of Schr\"odinger evolutions. We provide, in addition, an…
We prove a logarithmic convexity result for exponentially weighted $L^2$-norms of solutions to electromagnetic Schr\"odinger equation, without needing to assume smallness of the magnetic potential. As a consequence, we can prove a unique…
We shed new light on Heisenberg's uncertainty principle in the sense of Beurling, by offering an essentially different proof which permits us to weaken the assumptions substantially, and examples show that the result is sharp. The proof…
Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…
We prove a new version of the Uncertainty Principle of the form $\int |f|^2 \lesssim \int_{E^c} |f|^2 + \int_{\Sigma ^c}|\hat f|^2 $ where the sets $E$ and $\Sigma$ are $\epsilon$-thin in the following sense: $|E \cap D(x, \rho_1(x))| \le…
The aim of this paper is to prove an uncertainty principle for the representation of a vector in two bases. Our result extends previously known qualitative uncertainty principles into quantitative estimates. We then show how to transfer…
The purpose of this article is to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform (QFT). We study some fundamental properties of this extension such as scaling, translation,…
In this note, an alternative approach to establish observability for semigroups based on their smoothing properties is presented. The results discussed here are closely related to those recently obtained in [arXiv:2112.01788], but the…
Starting with the first-order singular Lagrangian describing the dynamical system with 2nd-class constraints, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of…
We discuss the concept of measurement in cosmology from the relativistic and quantum mechanical points of view. The uncertainty principle within the particle horizon, excludes the momentum of particles to be less than $\pi\hbar H/c$. This…
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 offset linear canonical transform (OLCT) provides a more general framework for a number of well known linear integral transforms in signal processing and optics, such as Fourier transform, fractional Fourier transform, linear canonical…
The main goal of this paper is to generalize the Sobolev-type inequalities given by Guo-Phong-Song-Sturm and Guedj-T\^o from the case of functions to the framework of twisted differential forms. To this end, we establish certain estimates…
We give a real-variable proof of the Hardy uncertainty principle. The method is based on energy estimates for evolutions with positive viscosity, convexity properties of free waves with Gaussian decay at two different times, elliptic…
Horndeski theory is the most general scalar-tensor extension of General Relativity with second order field equations. It may be interesting to study the effects of the Generalized Uncertainty Principle on a static and asymptotically flat…