Kazunori Ando

Spectral Properties of Schrödinger Operators on Perturbed Lattices

We study the spectral properties of Schrödinger operators on perturbed lattices. We shall prove the non-existence or the discreteness of embedded eigenvalues, the limiting absorption principle for the resolvent, construct a spectral representation, and define the S-matrix. Our theory covers the square, triangular, diamond, Kagome lattices, as well as the ladder, the graphite and the subdivision of square lattice.

Spectrum of Neumann--Poincaré Operator on Annuli and Cloaking by Anomalous Localized Resonance for Linear Elasticity

We investigate anomalous localized resonance on the circular coated structure and cloaking due to it in the context of elastostatic systems. The structure consists of the circular core with constant Lame parameters and the circular shell with negative Lame parameters proportional to those of the core. We show that there is a nonzero number

Inverse Scattering for Schrödinger Operators on Perturbed Lattices

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Analysis of plasmon resonance on smooth domains using spectral properties of the Neumann–Poincaré operator

determined by Lame parameters such that two nonempty eigenvalue sequences of the Neumann--Poincare operator associated with the structure converge to

Plasmon Resonance with Finite Frequencies: a Validation of the Quasi-static Approximation for Diametrically Small Inclusions

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Spectral properties of the Neumann–Poincaré operator and cloaking by anomalous localized resonance for the elasto-static system

and

Plasmon Resonance with Finite Frequencies

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Elastic Neumann–Poincaré Operators on Three Dimensional Smooth Domains: Polynomial Compactness and Spectral Structure

, respectively, and derive precise asymptotics of the convergence. We then show by qualitative estimates based on asymptotics of eigenvalues that cloaking by anomalous localized resonance takes place if and only if the dipole-type source lies inside critical radii determined by radii of the core and the shell. The critical radii corresponding to

Exponential decay estimates of the eigenvalues for the Neumann-Poincar\'e operator on analytic boundaries in two dimensions

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The first Hadamard variation of Neumann-Poincaré eigenvalues on the sphere

and