10 citations · 34 across the 13 of their papers we have counts for
15 papers
On the resolvent convergence of discrete Dirac operators on 3D cubic lattices
Karl Michael Schmidt, Tomio Umeda
We prove that the discrete Dirac operators in three dimensions converge to the continuum Dirac operators in the strong resolvent sense, but not in the norm resolvent sense.
Continuum limits for discrete Dirac operators on 2D square lattices
Karl Michael Schmidt, Tomio Umeda
We discuss the continuum limit of discrete Dirac operators on the square lattice in as the mesh size tends to zero. To this end, we propose the most natural and simpl…
On some integral operators appearing in scattering theory, and their resolutions
S. Richard, T. Umeda
We discuss a few integral operators and provide expressions for them in terms of smooth functions of some natural self-adjoint operators. These operators appear in the context of s…
Spectral theory of first-order systems: from crystals to Dirac operators
Matania Ben-Artzi, Tomio Umeda
Let $$L_0=\suml_{j=1}^nM_j^0D_j+M_0^0,\,\,\,\,D_j=\frac{1}{i}\frac{\pa}{\paxj}, \quad x\in\Rn,$$ be a constant coefficient first-order partial differential system, where the matric…
Schroedinger operators with n positive eigenvalues: an explicit construction involving complex valued potentials
S. Richard, J. Uchiyama, T. Umeda
An explicit construction is provided for embedding n positive eigenvalues in the spectrum of a Schroedinger operator on the half-line with a Dirichlet boundary condition at the ori…
Schnol's theorem and spectral properties of massless Dirac operators with scalar potentials
Karl Michael Schmidt, Tomio Umeda
The spectra of massless Dirac operators are of essential interest e.g. for the electronic properties of graphene, but fundamental questions such as the existence of spectral gaps r…