Asymptotic behavior of singular values of the acoustic observation problem

TL;DR

This paper analyzes the asymptotic behavior of singular values in the acoustic observation problem, which involves recovering initial data from boundary measurements in a wave equation setting.

Contribution

It provides the asymptotic analysis of singular values for the boundary observation operator in the wave equation, advancing understanding of the problem's spectral properties.

Findings

Asymptotic formulas for singular values are derived.

Results enhance the theoretical understanding of inverse boundary problems.

The analysis aids in the development of stable reconstruction methods.

Abstract

We consider the problem of recovering of initial data in the IBVP for the wave-type equation in the half-space by the solution restricted to the boundary. The singular value decomposition of this problem is concerned: the asymptotics of singular values is obtained.