Discrete observability and Dirichlet series (Q1092847)

The authors consider the problem of recovering the initial data of the heat equation in a bounded domain with standard boundary conditions, by output measurements, discrete in time and space. Using properties of Dirichlet series, they obtain a necessary and sufficient condition of observability. These conditions involve the multiplicity of the eigenvalues of the Laplace operator and a set of matrix rank conditions. The result generalizes previous ones. Some other extensions are indicated.