Observability of Laplace equation on the circle
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In this thesis, the problem of discrete observability of the Laplace equation is studied. It turns out that the solution of this problem can be uniquely determined by the measured values at certain dense set on the boundary. For the purpose of practical application, two methods are investigated. The first method, by means of distribution, shows that in any compact set inside the unit disk the real solution can be successfully approximated by the interpolation polynomials. The second method is simply solving a system of linear equations, while the speed of its convergence still remains unknown.