Titlebook: Spectral Geometry and Inverse Scattering Theory; Huaian Diao,Hongyu Liu Book 2023 The Editor(s) (if applicable) and The Author(s), under e

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e geometrical inverse shape problems by minimal measurements.Inverse scattering problems are a vital subject for both theoretical and experimental studies and remain an active field of research in applied mathematics. This book provides a detailed presentation of typical setup of inverse scattering

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Introduction,tion that seeks to optimally combine theory with observations. In its abstract formulation, an inverse problem can be described as follows. Let (., ∥⋅∥.) denote the space of target objects (usually consisting of quantities or geometries) and (., ∥⋅∥.) denote the space of observation data. Let . deno

Concrete

Geometric Structures of Maxwellian Eigenfunctions,ongly motivated by our study of the inverse electromagnetic scattering problem. In this chapter, we follow the treatment in Diao et al. (Inverse Probl 37:035004, 2021). Further discussion on the inverse electromagnetic scattering problems can be found in Sect. .. We start with the necessary mathemat

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Path Argument for Inverse Acoustic and Electromagnetic Obstacle Scattering Problems,nd . to represent the incident, scattered and total field, respectively, where . = . + . and . with . being the incident direction and . > 0 being the wave number. Let . be an impenetrable obstacle, where . is a general compact set in . with an open connect complement ..

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,Geometric Structures of Maxwell’s Transmission Eigenfunctions and Applications,–2224 (2021)). Let . denote the frequency, and let ., respectively, signify the electric permittivity and magnetic permeability of a uniformly homogeneous space. Throughout, we let . and . denote, respectively, the electric and magnetic fields, which are .-valued functions. We first introduce the no

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