59 citations · 151 across the 21 of their papers we have counts for
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A remark on the absence of eigenvalues in continuous spectra for discrete Schrödinger operators on periodic lattices
Kazunori Ando, Hiroshi Isozaki, Hisashi Morioka
We prove a Rellich-Vekua type theorem for Schrödinger operators with exponentially decreasing potentials on a class of lattices including square, triangular, hexagonal lattices and…
Complex translation methods and its application to resonances for quantum walks
Kenta Higuchi, Hisashi Morioka
In this paper, some properties of resonances for multi-dimensional quantum walks are studied. Resonances for quantum walks are defined as eigenvalues of complex translated time evo…
Resonances in finitely perturbed quantum walks, resonance expansion and generic simplicity
Kenta Higuchi, Hisashi Morioka, Etsuo Segawa
We define resonances for finitely perturbed quantum walks as poles of the scattering matrix in the lower half plane. We show a resonance expansion which describes the time evolutio…
Generalized eigenfunctions and scattering matrices for position-dependent quantum walks
Hisashi Morioka
We study the spectral analysis and the scattering theory for time evolution operators of position-dependent quantum walks. Our main purpose of this paper is construction of general…
Detection of edge defects by embedded eigenvalues of quantum walks
Hisashi Morioka, Etsuo Segawa
We consider a position-dependent quantum walk on . In particular, we derive a detection method for edge defects by embedded eigenvalues of its time evolution operator. In…
Inverse scattering for Schrödinger operators on perturbed lattices
Kazunori Ando, Hiroshi Isozaki, Hisashi Morioka
We study the inverse scattering for Schr{ö}dinger operators on locally perturbed periodic lattices. We show that the associated scattering matrix is equivalent to the Dirichlet-to-…
Interior transmission eigenvalue problems on compact manifolds with boundary conductivity parameters
Hisashi Morioka, Naotaka Shoji
In this paper, we consider an interior transmission eigenvalue (ITE) problem on some compact -Riemannian manifolds with a common smooth boundary. In particular, these…
Spectral Properties of Schrödinger Operators on Perturbed Lattices
Kazunori Ando, Hiroshi Isozaki, Hisashi Morioka
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 absorpti…
Inverse scattering at a fixed energy for discrere Schrödinger operators on the square lattice
Hiroshi Isozaki, Hisashi Morioka
We study an inverse scattering problem for the discrete Schrödinger operator on the multi-dimensional square lattice, with compactly supported potential. We show that the potential…
A Rellich Type Theorem for Discrete Schr{ö}dinger Operators
Hiroshi Isozaki, Hisashi Morioka
An analogue of Rellich's theorem is proved for discrete Laplacian on square lattice, and applied to show unique continuation property on certain domains as well as non-existence of…