This volume grew out of a workshop on spectral theory of differential operators and inverse problems held at the Research Institute for Mathematical Sciences (Kyoto University). The gathering of nearly 100 participants at the conference suggests the increasing interest in this field of research. The focus of the book is on spectral theory for differential operators and related inverse problems. It includes selected topics from the following areas: electromagnetism, elasticity, the Schrodinger equation, differential geometry, and numerical analysis. The material is suitable for graduate students and researchers interested in inverse problems and their applications.
On the determination of wave speed and potential in a hyperbolic equation by two measurements by V. G. Romanov and M. Yamamoto Focusing waves in electromagnetic inverse problems by Y. Kurylev, M. Lassas, and E. Somersalo Reconstruction of conductivity inhomogeneities of small diameter via boundary measurements by H. Ammari and H. Kang Unique determination of inhomogeneity in a stationary isotropic Lame system with variable coefficients by S. Kim and M. Yamamoto Mittag-Leffler's function and extracting from Cauchy data by M. Ikehata On the inverse boundary value problem for linear isotropic elasticity and Cauchy-Riemann systems by G. Eskin and J. Ralston Pointwise reconstruction of the jump at the boundaries of inclusions by M. Ikehata and G. Nakamura Constant parameters identification problems of coupled sine-Gordon equations by S.-i. Nakagiri and J. Ha Inverse problem for harmonic oscillator perturbed by potential by D. Chelkak, P. Kargaev, and E. Korotyaev Some transforms in potential scattering in odd dimension by A. Melin Inverse problems in $N$-body scattering by G. Uhlmann and A. Vasy Asymptotics of heat kernels on nilpotent coverings and related topics by A. Katsuda Eigenvalues associated with a periodic orbit of the magnetic flow by R. Kuwabara Inverse problems and hyperbolic manifolds by H. Isozaki Reconstruction of measurable plane sets from their orthogonal projections by T. Takiguchi A numerical computation for inverse boundary value problems by using the adjoint method by K. Iijima, K. Shirota, and K. Onishi The Dirichlet eigenvalue problem, the finite element method and graph theory by H. Urakawa A numerical method for the discontinuous solutions of Abel integral equations by J. Cheng, Y. C. Hon, and Y. B. Wang.