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

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U2 - 10.1017/S1446788713000311

DO - 10.1017/S1446788713000311

M3 - Article

AN - SCOPUS:84893680843

VL - 95

SP - 297

EP - 314

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

IS - 3

ER -