scholarly journals Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation

1990 ◽  
Vol 40 (2) ◽  
pp. 313-356 ◽  
Author(s):  
Nicola Garofalo ◽  
Ermanno Lanconelli
Keyword(s):  
Heisenberg Group ◽  
Uncertainty Principle ◽  
Unique Continuation ◽  
Frequency Functions

scholarly journals Hardy uncertainty principle and unique continuation properties of covariant Schrödinger flows

2013 ◽  
Vol 264 (10) ◽  
pp. 2386-2415 ◽  
Author(s):  
J.A. Barceló ◽  
L. Fanelli ◽  
S. Gutiérrez ◽  
A. Ruiz ◽  
M.C. Vilela
Keyword(s):  
Uncertainty Principle ◽  
Unique Continuation

HARDY AND MIYACHI THEOREMS FOR HEISENBERG MOTION GROUPS

2016 ◽  
Vol 229 ◽  
pp. 1-20 ◽  
Author(s):  
ALI BAKLOUTI ◽  
SUNDARAM THANGAVELU
Keyword(s):  
Heisenberg Group ◽  
Uncertainty Principle ◽  
Price Uncertainty ◽  
Motion Group ◽  
Hardy’S Theorem ◽  
Motion Groups ◽  
Miyachi’S Theorem

Let $G=\mathbb{H}^{n}\rtimes K$ be the Heisenberg motion group, where $K=U(n)$ acts on the Heisenberg group $\mathbb{H}^{n}=\mathbb{C}^{n}\times \mathbb{R}$ by automorphisms. We formulate and prove two analogues of Hardy’s theorem on $G$. An analogue of Miyachi’s theorem for $G$ is also formulated and proved. This allows us to generalize and prove an analogue of the Cowling–Price uncertainty principle and prove the sharpness of the constant $1/4$ in all the settings.

scholarly journals Hardy’s uncertainty principle and unique continuation property for stochastic heat equations

2020 ◽  
Vol 26 ◽  
pp. 9
Author(s):  
Aingeru Fernández-Bertolin ◽  
Jie Zhong
Keyword(s):  
Heat Equation ◽  
Uncertainty Principle ◽  
Unique Continuation ◽  
Stochastic Heat Equation ◽  
Heat Equations ◽  
Unique Continuation Property ◽  
Stochastic Heat Equations ◽  
Continuation Property

The goal of this paper is to prove a qualitative unique continuation property at two points in time for a stochastic heat equation with a randomly perturbed potential, which can be considered as a variant of Hardy’s uncertainty principle for stochastic heat evolutions.

THE UNIQUE CONTINUATION PROPERTY OF -HARMONIC FUNCTIONS ON THE HEISENBERG GROUP

2018 ◽  
Vol 99 (2) ◽  
pp. 219-230 ◽  
Author(s):  
HAIRONG LIU ◽  
FANG LIU ◽  
HUI WU
Keyword(s):  
Heisenberg Group ◽  
Laplace Equation ◽  
Harmonic Functions ◽  
Unique Continuation ◽  
Frequency Function ◽  
Unique Continuation Property ◽  
Continuation Property

We introduce an Almgren frequency function of the sub-$p$-Laplace equation on the Heisenberg group to establish a doubling estimate under the assumption that the frequency function is locally bounded. From this, we obtain some partial results on unique continuation for the sub-$p$-Laplace equation.

scholarly journals Variations on a theorem of Cowling and Price with applications to nilpotent Lie groups

2007 ◽  
Vol 82 (1) ◽  
pp. 11-27 ◽  
Author(s):  
S. Parui ◽  
S. Thangavelu
Keyword(s):  
Heisenberg Group ◽  
Lie Groups ◽  
Uncertainty Principle ◽  
Fourier Transforms ◽  
Nilpotent Lie Groups

AbstractIn this paper we prove a new version of the Cowling-Price theorem for Fourier transforms on Rn. Using this we formulate and prove an uncertainty principle for operators. This leads to an analogue of the Cowling-Price theorem for nilpotent Lie groups. We also prove an exact analogue of the Cowling-Price theorem for the Heisenberg group.

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