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

Abstract

Let be a complete metric space and let be a Borel measure on . Under certain fairly general assumptions about the metric and the measure, we use lattice theory to construct an isometric copy of the space , 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.