New notions and constructions of the boundary control method

M. I. Belishev

doi:10.3934/ipi.2022040

Article Contents

2022, Volume 16, Issue 6: 1447-1471. Doi: 10.3934/ipi.2022040

This issue Previous Article On the scientific work of Victor Isakov Next Article A spectral target signature for thin surfaces with higher order jump conditions

New notions and constructions of the boundary control method

M. I. Belishev^,

Saint-Petersburg Department of Steklov Mathematical Institute, Russian Academy of Sciences, Russia

^*Corresponding author: M. I. Belishev
^*Corresponding author: M. I. Belishev

In memory of Victor Isakov

Received: December 2021

Revised: June 2022

Early access: July 27, 2022

Published online: July 27, 2022

The author is supported by RFBR grant 20-01 627A.

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Abstract

The paper provides a list of mathematical objects, constructions and notions, which were revealed and introduced in the course of creation and development of the boundary control method. Among them, there are: amplitude integral, equidistant transforms of 3d vector fields, $ s $-points in acoustic scattering, formulas for Betti numbers via DN-map, eikonal algebras, wave spectrum of symmetric semi-bounded operator. We describe these objects and explain how they work for solving inverse problems.

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Mathematics Subject Classification: Primary: 35R30, 47Axx, 46J10, 30Fxx, 35R25.

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