Geodesic
The wave model of a~metric space with measure and an application
Sbornik. Mathematics, Tome 211 (2020) no. 4, pp. 521-538

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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.
Keywords: metric space, measure, isotony, wave model, reconstruction of a Riemannian manifold. 
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     author = {M. I. Belishev and S. A. Simonov},
     title = {The wave model of a~metric space with measure and an application},
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M. I. Belishev; S. A. Simonov. The wave model of a~metric space with measure and an application. Sbornik. Mathematics, Tome 211 (2020) no. 4, pp. 521-538. http://geodesic.mathdoc.fr/item/SM_2020_211_4_a2/