Related papers: Qualitative uncertainty principles for the windowe…
In this paper, we uncover a new uncertainty principle that governs the complexity of Boolean functions. This principle manifests as a fundamental trade-off between two central measures of complexity: a combinatorial complexity of its…
The aim of this paper is to prove new uncertainty principles for an integral operator $\tt$ with a bounded kernel for which there is a Plancherel theorem. The first of these results is an extension of Faris's local uncertainty principle…
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…
In this paper, we study a few versions of the uncertainty principle for the short-time Fourier transform on the lattice $\mathbb Z^n \times \mathbb T^n$. In particular, we establish the uncertainty principle for orthonormal sequences,…
We show in this paper that the basic representations of position and momentum in a quantum mechanical system, that are guided by a generalized uncertainty principle and lead to a corresponding one-parameter eigenvalue problem, can be…
In this paper we obtain Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities with sharp constants on Riemannian manifolds with non-positive sectional curvature and, in particular, a variety of new estimates on…
We provide new uncertainty principles for functions in a general class of Gelfand-Shilov spaces. These results apply, in particular, with the classical Gelfand-Shilov spaces as well as for spaces of functions with weighted Hermite…
In this paper, we generalize the continuous quaternion shearlet transform on $\mathbb{R}^{2}$ to $\mathbb{R}^{2d}$, called the multivariate two sided continuous quaternion shearlet transform. Using the two sided quaternion Fourier…
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…
In this article we prove both norm and modular Hardy inequalities for a class functions in one-dimensional fractional Orlicz-Sobolev spaces.
In this paper, some properties on weighted modulation and Wiener amalgam spaces are characterized by the corresponding properties on weighted Lebesgue spaces. As applications, sharp conditions for product inequalities, convolution…
In this paper, we study Hardy-type uncertainty principles and unique continuation properties for linear covariant Schrodinger equations with variable coefficients in the presence of bounded electric and magnetic potentials. Under suitable…
Some properties of the $q$-Fourier-sine transform are studied and $q$-analogues of the Heisenberg uncertainty principle is derived for the $q$-Fourier-cosine transform studied in \cite{FB} and for the $q$-Fourier-sine transform.
In this paper, we estabish an analogue of Hardy's theorem and Miyachi's theorem for the Clifford-Fourier transform.
We study the Cauchy problem for fractional Schr\"odinger equation with cubic convolution nonlinearity ($i\partial_t u - (-\Delta)^{\frac{\alpha}{2}}u\pm (K\ast |u|^2) u =0$) with Cauchy data in the modulation spaces $M^{p,q}(\mathbb…
Modified uncertainty principle and non-commutative variables may phenomenologically account for quantum gravity effects, independently of the considered theory of quantum gravity. We show that quantum fluids enable experimental analogs and…
The Schrodinger equation is incomplete, inherently unable to explain the collapse of the wavefunction caused by measurement; a fundamental issue known as the quantum measurement problem. Quantum mechanics is generally constrained by the…
Some fundamental aspects related with the construction of Robertson-Schr\"odinger like uncertainty principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum…
We introduce a complete analytical and numerical study of the modulational instability process in a system governed by a canonical nonlinear Schr\"odinger equation involving local, arbitrary nonlinear responses to the applied field. In…
The aim of this article is to formulate some novel uncertainty principles for the continuous shearlet transforms in arbitrary space dimensions. Firstly, we derive an analogue of the Pitt's inequality for the continuous shearlet transforms,…