Related papers: Noncommutative Uncertainty Principles
The Hausdorff-Young inequality for Euclidean space, in its sharp form due to Beckner, gives an upper bound for the Fourier transform in terms of Lebesgue space norms, with an optimal constant. The extremizers have been identified by Lieb to…
Let $\mathcal{X}$ be a 3-product space. Let $A: \mathcal{D}(A)\subseteq \mathcal{X}\to \mathcal{X}$, $B: \mathcal{D}(B)\subseteq \mathcal{X}\to \mathcal{X}$ and $C: \mathcal{D}(C)\subseteq \mathcal{X}\to \mathcal{X}$ be possibly unbounded…
We generalize, improve and unify theorems of Rumin, and Maassen--Uffink about classical entropies associated to quantum density matrices. These theorems refer to the classical entropies of the diagonals of a density matrix in two different…
Classical results due to Ingham and Paley-Wiener characterize the existence of nonzero functions supported on certain subsets of the real line in terms of the pointwise decay of the Fourier transforms. We view these results as uncertainty…
Recently Kosaki proved an inequality for matrices that can be seen as a kind of new uncertainty principle. Independently, the same result was proved by Yanagi, Furuichi and Kuriyama. The new bound is given in terms of Wigner-Yanase-Dyson…
A sharper uncertainty inequality which exhibits a lower bound larger than that in the classical N-dimensional Heisenberg's uncertainty principle is obtained, and extended from N-dimensional Fourier transform domain to two N-dimensional…
We introduce a notion of localization for dyadic functions, i.e. functions defined on the Cantor group. Localization is characterized by functional $UC_d$ similar to the Heisenberg uncertainty constant used for real-line functions. We are…
Chebotar\"ev proved that every minor of a discrete Fourier matrix of prime order is nonzero. We prove a generalization of this result that includes analogues for discrete cosine and discrete sine matrices as special cases. We establish…
In this article, the Heisenberg-Pauli-Weyl uncertainty principle and Donoho-Stark s uncertainty principle are obtained for the Poly-axially L 2 {\alpha} -multiplier operators
We establish anisotropic uncertainty principles (UPs) for general metaplectic operators acting on $L^2(\mathbb{R}^d)$, including degenerate cases associated with symplectic matrices whose $B$-block has nontrivial kernel. In this setting,…
The Heisenberg uncertainty principle is one of the fundamental pillars of quantum mechanics and quantum field theory. It is normally introduced by postulating the commutation relations $[\hat{x}^i, \hat{p}^j] = i\hbar \delta^{ij}$. However,…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
Classical and recent results on uncertainty principles for functions on finite Abelian groups relate the cardinality of the support of a function to the cardinality of the support of its Fourier transforms. We use these results and their…
As a time-shifted and frequency-modulated version of the linear canonical transform (LCT), the offset linear canonical transform (OLCT) provides a more general framework of most existing linear integral transforms in signal processing and…
We study modular forms for the minimal index noncongruence subgroups of the modular group. Our main theorem is a proof of the unbounded denominator conjecture for these groups, and we also provide a study of the Fourier coefficients of…
Khosravi, Drnov\v{s}ek and Moslehian [\textit{Filomat, 2012}] derived Buzano inequality for Hilbert C*-modules. Using this inequality we derive Deutsch entropic uncertainty principle for Hilbert C*-modules over commutative unital…
The Weinstein operator has several applications in pure and applied Mathematics especially in Fluid Mechanics and satisfies some uncertainty principles similar to the Euclidean Fourier transform. The aim of this paper is establish a…
The paper studies Hausdorff-Young inequalities for certain group extensions, by use of Mackey's theory. We consider the case in which the dual action of the quotient group is free almost everywhere. This result applies to yield a…
We consider the families of finite Abelian groups $\ZZ/p\ZZ\times \ZZ/p\ZZ$, $\ZZ/p^2\ZZ$ and $\ZZ/p\ZZ\times \ZZ/q\ZZ$ for $p,q$ two distinct prime numbers. For the two first families we give a simple characterization of all functions…
Let $G$ be a finite abelian group, and let $f: G \to \C$ be a complex function on $G$. The uncertainty principle asserts that the support $\supp(f) := \{x \in G: f(x) \neq 0\}$ is related to the support of the Fourier transform $\hat f: G…