Uniqueness of solutions to schrödingera equations on H-type groups

Salem Ben Saïd, Sundaram Thangavelu, Venku Naidu Dogga

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)297-314
Number of pages18
JournalJournal of the Australian Mathematical Society
Issue number3
Publication statusPublished - Dec 2013
Externally publishedYes


  • H-type groups
  • Heat kernel
  • Schrödinger equation
  • Spherical harmonics
  • Sub-Laplacian

ASJC Scopus subject areas

  • General Mathematics


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