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In this paper, we give a harmonic analysis proof of the Neumann boundaryobservability inequality for the wave equation in an arbitrary space dimension.Our proof is elementary in nature and gives a simple, explicit constant. Wealso extend the method to prove the observability inequality of a visco-elasticwave equation.

A Harmonic Analysis Proof of the Boundary Observability Inequality for the Wave Equation and Visco-Elastic Equation