Uncertainty relations on nilpotent Lie groups

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Title: Uncertainty relations on nilpotent Lie groups
Authors: Ruzhansky, M
Suragan, D
Item Type: Journal Article
Abstract: We give relations between main operators of quantum mechanics on one of most general classes of nilpotent Lie groups. Namely, we show relations between momentum and position operators as well as Euler and Coulomb potential operators on homogeneous groups. Homogeneous group analogues of some well-known inequalities such as Hardy's inequality, Heisenberg–Kennard type and Heisenberg–Pauli–Weyl type uncertainty inequalities, as well as Caffarelli–Kohn–Nirenberg inequality are derived, with best constants. The obtained relations yield new results already in the setting of both isotropic and anisotropic Rn, and of the Heisenberg group. The proof demonstrates that the method of establishing equalities in sharper versions of such inequalities works well in both isotropic and anisotropic settings.
Issue Date: 21-May-2017
Date of Acceptance: 13-Apr-2017
ISSN: 1471-2946
Publisher: Royal Society, The
Journal / Book Title: Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences
Volume: 473
Issue: 2201
Copyright Statement: © 2017 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License, which permits unrestricted use, provided the original author and source are credited.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Funder's Grant Number: EP/K039407/1
Keywords: homogeneous Lie group
nilpotent Lie group
uncertainty principle
81S99, 22E30, 46C99
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status: Published
Article Number: 20170082
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences

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