We prove various Hardy-type and uncertainty inequalities on a stratified Lie group G. In
particular, we show that the operators T α: f↦|⋅|− α L− α/2 f, where|⋅| is a homogeneous …

We obtain several versions of the Hausdorff–Young and Hardy–Littlewood inequalities for
the (k, a)-generalized Fourier transform recently investigated at length by Ben Saïd …

We present a model of discrete quantum evolution based on quantum correlations between
the evolving system and a reference quantum clock system. A quantum circuit for the model …

We discuss some fundamental properties of discrete system-time history states. Such states
arise for a quantum reference clock of finite dimension and lead to a unitary evolution of …

In this paper we revisit the Bialynicki-Birula and Mycielski uncertainty principle and its cases
of equality. This Shannon entropic version of the well-known Heisenberg uncertainty …

The classical uncertainty principles deal with functions on abelian groups. In this paper, we
discuss the uncertainty principles for finite index subfactors which include the cases for finite …

The traditional Heisenberg–Weyl measure quantifies the joint localization, uncertainty, or
concentration of a signal in the phase plane based on a product of energies expressed as …

In this paper, we prove the Donoho–Stark uncertainty principle for locally compact quantum
groups and characterize the minimizer which are bi-shifts of group-like projections. We also …

The fundamental properties of quantum physics are exploited to evaluate event probabilities
with projection measurements. Next, to study what events can be specified by quantum …

We consider the maximal rank-deficient submatrices of Fourier matrices with order a power
of a prime number. We do this by considering a hierarchical subdivision of these matrices …