TY - JOUR

T1 - The wave model of a metric space with measure and an application

AU - Belishev, M. I.

AU - Simonov, S. A.

N1 - Publisher Copyright: © 2020 Russian Academy of Sciences (DoM) and London Mathematical Society.

PY - 2020/4

Y1 - 2020/4

N2 - Let (Ω,d) be a complete metric space and let µ be a Borel measure on Ω. Under certain fairly general assumptions about the metric and the measure, we use lattice theory to construct an isometric copy (Ωe,de) of the space (Ω,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.

AB - Let (Ω,d) be a complete metric space and let µ be a Borel measure on Ω. Under certain fairly general assumptions about the metric and the measure, we use lattice theory to construct an isometric copy (Ωe,de) of the space (Ω,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.

KW - Isotony

KW - Measure

KW - Metric space

KW - Reconstruction of a riemannian manifold

KW - Wave model

UR - http://www.scopus.com/inward/record.url?scp=85087459719&partnerID=8YFLogxK

U2 - 10.1070/SM9242

DO - 10.1070/SM9242

M3 - Article

AN - SCOPUS:85087459719

VL - 211

SP - 521

EP - 538

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 4

ER -