# UNIQUENESS OF SOLUTIONS TO SCHRODINGER EQUATIONS ON H-TYPE GROUPS

Ben Said, Salem and Thangavelu, Sundaram and Dogga, Venku Naidu (2014) UNIQUENESS OF SOLUTIONS TO SCHRODINGER EQUATIONS ON H-TYPE GROUPS. In: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 95 (3). pp. 297-314.

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Official URL: http://dx.doi.org/10.1017/S1446788713000311

## Abstract

This paper deals with the Schrodinger equation i partial derivative(s)u(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 vertical bar f(z, t)vertical bar less than or similar to q(alpha)(z, t), where q(s) is the heat kernel associated to L. If in addition vertical bar u(z, t; s(0))vertical bar less than or similar to q(beta)(z, t), for some s(0) is an element of R \textbackslash {0}, then we prove that u(z, t; s) = 0 for all s is an element of R whenever alpha beta < s(0)(2). 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.

Item Type: Journal Article JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY CAMBRIDGE UNIV PRESS copyright for this article belongs to CAMBRIDGE UNIV PRESS, 32 AVENUE OF THE AMERICAS, NEW YORK, NY 10013-2473 USA H-type groups; sub-Laplacian; Schrodinger equation; heat kernel; spherical harmonics Division of Physical & Mathematical Sciences > Mathematics 18 Jun 2014 03:58 18 Jun 2014 03:58 http://eprints.iisc.ac.in/id/eprint/49270