Related papers: Unbounded operators and the uncertainty principle
The aim of this paper is establish the Heisenberg-Pauli-Weyl uncertainty principle and Donho-Stark's uncertainty principle for the Weinstein $L^2$-multiplier operators.
Consider the pseidounitary group $G=U(p,q)$ and its compact subgroup $K=U(p)$. We construct an explicit unitary intertwining operator from the tensor product of a holomorphic representation and a antiholomorphic representation of $G$ to the…
In this paper, we extend the concept of absolutely Ces\`aro boundedness to the fractional case. We construct a weighted shift operator belonging to this class of operators, and we prove that if $T$ is an absolutely Ces\`{a}ro bounded…
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…
A sharp version of the Balian-Low theorem is proven for the generators of finitely generated shift-invariant spaces. If generators $\{f_k\}_{k=1}^K \subset L^2(\mathbb{R}^d)$ are translated along a lattice to form a frame or Riesz basis for…
One of the advantages of a reconstruction of quantum mechanics based on transparent physical axioms is that it may offer insight to naturally generalize quantum mechanics by relaxing the axioms. Here, we discuss possible extensions of…
In this paper we introduce the Schatten class of operators and the Berezin transform of operators in the quaternionic setting. The first topic is of great importance in operator theory but it is also necessary to study the second one…
We construct bounded pseudoconvex domains in $\mathbb{C}^2$ for which the Szeg\"o projection operators are unbounded on $L^p$ spaces of the boundary for all $p\not =2$.
In this manuscript, we introduce the quadratic--phase Fourier--Bessel transform and develop its foundational properties, including continuity, the Riemann--Lebesgue lemma, reversibility, and Parseval's identity. We define the associated…
In this paper, we establish the Cowling--Price's, Hardy's and Morgan's uncertainty principles for the Opdam-Cherednik transform on modulation spaces associated with this transform. The proofs of the theorems are based on the properties of…
In this paper, we study noncommutative varieties in polydomains in $B(H)^n$. The goal is to understand the structure of these varieties, determine their elements and classify them up to unitary equivalence. Using noncommutative Berezin…
We give embedding theorems for weighted Bergman-Orlicz spaces on the ball and then apply our results to the study of composition operators in this context. As one of the motivations of this work, we show that there exist some weighted…
In this article, we establish the Berezin number and Berezin norm inequalities for bounded linear operators on a reproducing kernel Hilbert space using the Moore-Penrose inverse. The inequalities obtained here refine and generalize the…
Extending a recent result by Frank and Lieb, we show an entropic uncertainty principle for mixed states in a Hilbert space relatively to pairs of positive operator valued measures that are independent in some sense. This yields…
We extend the well-known Katznelson-Tzafriri theorem, originally posed for power-bounded operators, to the case of Ces\`aro bounded operators of any order $\alpha>0.$ For this purpose, we use a functional calculus between a new class of…
This is our third work on Bergman-type operator over bounded domains. In the previous two articles, we systematically study the boundedness, compactness and Schatten membership of Bergman-type on the Hilbert unit ball. In the present paper,…
We extend the recent results concerning boundedness of the maximal regularity operator on tent spaces. This leads us to develop a singular integral operator theory on tent spaces. Such operators have operator-valued kernels. A seemingly…
A linear operator $U$ acting boundedly on an infinite-dimensional separable complex Hilbert space $H$ is universal if every linear bounded operator acting on $H$ is similar to a scalar multiple of a restriction of $U$ to one of its…
In this paper we introduce reproducing kernel Hilbert spaces of polyanalytic functions of infinite order. First we study in details the counterpart of the Fock space and related results in this framework. In this case the kernel function is…
This paper introduces a new family of semi-norms, say $\sigma_\mu$-Berezin norm on the space of all bounded linear operators $B(\mathcal{H})$ defined on a reproducing kernel Hilbert space $\mathcal{H}$, namely, for each $\mu \in [0,1]$ and…