Affiliation:
1. Department of Partial Differential Equations , [ 187495]The National Technical University of Ukraine, “Igor Sikorsky Kyiv Polytechnic Institute” , Kyiv , Ukraine
Abstract
Abstract
The generalization of Hardy uncertainty principle for the windowed Bochner–Fourier transform on the Heisenberg group is proved. We consider a Bochner measurable function
Ψ
:
G
→
X
{\Psi:G\to X}
, where X is a completely separable Hilbert space X and Let G be a completely separable, unimodular, connected nilpotent Lie group. We establish that if
ϕ
∈
C
C
(
G
)
{\phi\in C_{C}(G)}
is a non-trivial window function and
Ψ
∈
L
2
(
G
)
{\Psi\in L^{2}(G)}
satisfies
∥
V
ϕ
(
Ψ
)
(
g
,
χ
)
∥
HB
≤
c
2
(
g
)
exp
(
-
β
∥
χ
∥
2
)
\|V_{\phi}(\Psi)(g,\chi)\|_{\rm HB}\leq c_{2}(g)\exp(-\beta\|\chi\|^{2})
,
β
>
0
{\beta>0}
, then
Ψ
=
0
{\Psi=0}
almost everywhere.