The wave model of a metric space with measure and an application

Let $(\Omega,d)$ be a complete metric space and let $\mu$ be a Borel measure on $\Omega$. Under certain fairly general assumptions about the metric and the measure, we use lattice theory to construct an isometric copy $(\widetilde\Omega,\widetilde d)$ of the space $(\Omega,d)$, which is called its wave model. The construction is motivated by applications to inverse problems of mathematical physics. We show how the wave model solves the problem of reconstructing a Riemannian manifold with boundary from its spectral data.
Bibliography: 13 titles.