Inverse Boundary Spectral Problems (Hardcover)

INTRODUCTION

ONE-DIMENSIONAL INVERSE PROBLEM
The Problem and the Main Result
Wave Equation
Controllability and Projectors
Gaussian Beams

BASIC GEOMETRICAL AND ANALYTICAL METHODS FOR INVERSE PROBLEMS
Basic Tools of Riemannian Geometry for Inverse Problems
Elliptic Operators on Manifolds and Gauge Transformation
Initial-Boundary Value Problem for Wave Equation
Gaussian Beams
Carleman Estimates and Unique Continuation

GEL'FAND INVERSE BOUNDARY SPECTRAL PROBLEM FOR MANIFOLDS
Formulation of the Problem and the Main Result
Fourier Coefficients of Waves
Domains of Influence
Global Unique Continuation from the Boundary
Gaussian Beams from the Boundary
Domains of Influence and Gaussian Beams
Boundary Distance Functions
Reconstruction of the Riemannian Manifold
Reconstruction of the Potential

INVERSE PROBLEMS FOR WAVE AND OTHER TYPES OF EQUATIONS
Inverse Problems with Different Types of Data
Dynamical Inverse Problem for the Wave Equation
Continuation of Data
Inverse problems with Data Given on a Part of the Boundary
Inverse Problems for Operators in Rm

BIBLIOGRAPHY
TABLE OF NOTATION