T. Umeda

activity

19992025

most citedEigenfunctions at the threshold energies of magnetic Dirac operators

10 citations · 34 across the 13 of their papers we have counts for

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9 papers · 1 filter

math.SP2013★ 7 cited

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…

math.SP2011★ 2 cited

The Dirac-Hardy and Dirac-Sobolev inequalities in $L^{1}$

A. A. Balinsky, W. D. Evans, T. Umeda

Dirac-Sobolev and Dirac-Hardy inequalities in $L^{1}$ are established in which the $L^{p}$ spaces which feature in the classical Sobolev and Hardy inequalities are replaced by weak $L^…

math.SP2009★ 10 cited

Eigenfunctions at the threshold energies of magnetic Dirac operators

Yoshimi Saito, Tomio Umeda

Discussed are $\pm m$ modes and $\pm m$ resonances of Dirac operators with vector potentials $H_{A} = α \cdot (D - A (x)) + m β$ . Asymptotic limits of $\pm m$ modes at infinity are…

math.SP2008

Generalized eigenfunctions of relativistic Schroedinger operators in two dimensions

Tomio Umeda, Dabi Wei

Generalized eigenfunctions of the two-dimensional relativistic Schrödinger operator $H = - Δ + V (x)$ with $∣ V (x) ∣ \leq C < x >^{- σ}$ , $σ > 3/2$ , are considered. We compute the integra…

math.SP2008

Eigenfunctions of Dirac operators at the threshold energies

Tomio Umeda

We show that the eigenspaces of the Dirac operator $H = α \cdot (D - A (x)) + m β$ at the threshold energies $\pm m$ are coincide with the direct sum of the zero space and the kernel o…

math.SP2007★ 7 cited

The asymptotic limits of zero modes of massless Dirac operators