On the Uniqueness of Solutions of the Schrödinger Equation on Riemannian Symmetric Spaces of the Noncompact Type

Angela Pasquale; Maddala Sundari

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arXiv · 1011.1066

On the Uniqueness of Solutions of the Schrödinger Equation on Riemannian Symmetric Spaces of the Noncompact Type

Angela Pasquale·Maddala Sundari

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Abstract

Let X be a Riemannian symmetric space of the noncompact type. We prove that the solution of the time-dependent Schrödinger equation on X with square integrable initial condition f is identically zero at all times t whenever f and the solution at a time t0 > 0 are simultaneously very rapidly decreasing. The stated condition of rapid decrease is of Beurling type. Conditions respectively of Gelfand-Shilov, Cowling-Price and Hardy type are deduced.

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Angela Pasquale, Maddala Sundari. 2011-03-31. On the Uniqueness of Solutions of the Schrödinger Equation on Riemannian Symmetric Spaces of the Noncompact Type. https://arxiv.org/abs/1011.1066

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