Polar duality between pairs of transversal Lagrangian planes; applications to uncertainty principles

DOI10.1016/j.bulsci.2022.103171zbMath1495.52004OpenAlexW4285498563WikidataQ114200162 ScholiaQ114200162MaRDI QIDQ2166186

Maurice A. De Gosson

Publication date: 24 August 2022

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2022.103171

zbMATH Keywords

symplectic capacityLagrangian planeuncertainty principlepolar dualityJohn and Löwner ellipsoids

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Geometry and quantization, symplectic methods (81S10) Symplectic geometry, contact geometry (53D99) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Convex sets without dimension restrictions (aspects of convex geometry) (52A05)

Related Items

Pointillisme à la Signac and construction of a quantum fiber bundle over convex bodies, Geometric quantum states and Lagrangian polar duality: quantum mechanics without wavefunctions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Two geometric interpretations of the multidimensional Hardy uncertainty principle
• From symplectic measurements to the Mahler conjecture
• Symplectic topology and Hamiltonian dynamics. II
• Quantum states and Hardy's formulation of the uncertainty principle: a symplectic approach
• The symplectic camel and the uncertainty principle: the tip of an iceberg?
• Pseudo holomorphic curves in symplectic manifolds
• Symplectic topology and Hamiltonian dynamics
• Ellipsoids of maximal volume in convex bodies
• On a (no longer) new Segal algebra: a review of the Feichtinger algebra
• The Schur complement and its applications
• Quantum polar duality and the symplectic camel: a new geometric approach to quantization
• Symplectic geometry and quantum mechanics
• \(C^ *\)-algèbres des systèmes canoniques. I
• Advanced Concepts in Quantum Mechanics
• The Wigner Transform
• Symplectic Methods in Harmonic Analysis and in Mathematical Physics
• Conditions for the convolution of two Wigner distributions to be itself a Wigner distribution
• A Theorem Concerning Fourier Transforms
• Alice and Bob Meet Banach