TY - JOUR
T1 - Uniqueness of solutions to schrödingera equations on H-type groups
AU - Saïd, Salem Ben
AU - Thangavelu, Sundaram
AU - Dogga, Venku Naidu
N1 - Funding Information:
The work of the last two authors is supported by a J. C. Bose Fellowship from DST, India. 12 2013 07 08 2013 95 3 297 314 04 06 2011 19 05 2013 Copyright ©2013 Australian Mathematical Publishing Association Inc. 2013 Australian Mathematical Publishing Association Inc.
PY - 2013/12
Y1 - 2013/12
N2 - This paper deals with the Schrödinger equation i∂su(z, t; s) - Lu(z, t; s)= 0, where L is the sub-Laplacian on the Heisenberg group. Assume that the initial data f satisfies |f(z, t)| ≤ qa(z, t), where qs is the heat kernel associated to L. If in addition |u(z, t; s0) ≤ qβ (z, t), for some s0 ∈ R \ {0}, then we prove that u(z, t; s)= 0 for all s ∈ R whenever αβ < s02. This result holds true in the more general context of H-type groups. We also prove an analogous result for the Grushin operator on Rn+1.
AB - This paper deals with the Schrödinger equation i∂su(z, t; s) - Lu(z, t; s)= 0, where L is the sub-Laplacian on the Heisenberg group. Assume that the initial data f satisfies |f(z, t)| ≤ qa(z, t), where qs is the heat kernel associated to L. If in addition |u(z, t; s0) ≤ qβ (z, t), for some s0 ∈ R \ {0}, then we prove that u(z, t; s)= 0 for all s ∈ R whenever αβ < s02. This result holds true in the more general context of H-type groups. We also prove an analogous result for the Grushin operator on Rn+1.
KW - H-type groups
KW - Heat kernel
KW - Schrödinger equation
KW - Spherical harmonics
KW - Sub-Laplacian
UR - http://www.scopus.com/inward/record.url?scp=84893680843&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84893680843&partnerID=8YFLogxK
U2 - 10.1017/S1446788713000311
DO - 10.1017/S1446788713000311
M3 - Article
AN - SCOPUS:84893680843
SN - 1446-7887
VL - 95
SP - 297
EP - 314
JO - Journal of the Australian Mathematical Society
JF - Journal of the Australian Mathematical Society
IS - 3
ER -