Vector- valued distributions and Hardy's uncertainty principle for operators

2008/05/13 by Michael G. Cowling, Michael Cowling, Bruno Demange +5
Mathematics · #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis #math.CA #msc:43A32

paper · pdf · doi:10.48550/arxiv.0805.1807

10 pages

arxiv created 2008/05/13 · arxiv updated 2009/12/01

Abstract

In this paper, we generalise Hardy's uncertainty principle to vector-valued functions, and hence to operators. The principle for operators can be formulated loosely by saying that the kernel of an operator cannot be localised near the diagonal if the spectrum is also localised.

Related

• The Multi-Dimensional Hardy Uncertainty Principle and its Interpretation in Terms of the Wigner Distribution; Relation With the Notion of Symplectic Capacity
• Some remarks on vector valued distributions
• The Hardy Uncertainty Principle Revisited
• Remarks on the Fact that the Uncertainty Principle Does Not Determine the Quantum State
• Hardy's uncertainty principle and unique continuation properties for abstract Schrödinger equations