We survey various mathematical aspects of the uncertainty principle, including Heisenberg's
inequality and its variants, local uncertainty inequalities, logarithmic uncertainty inequalities …

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 …

There exists a generalized Hankel transform of order $\alpha\geq-1/2$ on $\mathbb {R} $,
which is based on the eigenfunctions of the Dunkl operator\[\qquad\quad\quad T_\alpha f …

Abstract Let Ω⊂ ℝ d have finite positive Lebesgue measure, and let L^ 2 (Ω) be the
corresponding Hilbert space of L^ 2-functions on Ω. We shall consider the exponential …

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 …

An uncertainty principle for the Dunkl transform Page 1 BULL. AUSTRAL. MATH. SOC. 33C80,
43A32, 42C15, 26D10 VOL. 59 (1999) [353-360] AN UNCERTAINTY PRINCIPLE FOR THE …

The aim of this paper is to prove new uncertainty principles for an integral operator with a
bounded kernel. To do so we prove a Nash-type inequality and a Carlson-type inequality for …

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In this paper, we extend a theorem of Hardy's on Fourier transform pairs to:(a) a noncompact-
type Riemannian symmetric space of rank one, with respect to the eigenfunction expansion …

A very general uncertainty principle is given for operators on Banach spaces. Many
consequences are derived, including uncertainty principles for Bessel sequences in Hilbert …