Open Access
October, 2011 Relativistic Hamiltonians with dilation analytic potentials diverging at infinity
Hiroshi T. ITO, Osanobu YAMADA
J. Math. Soc. Japan 63(4): 1311-1357 (October, 2011). DOI: 10.2969/jmsj/06341311


We investigate the spectral properties of the Dirac operator with a potential V(x) and two relativistic Schrödinger operators with V(x) and -V(x), respectively. The potential V(x) is assumed to be dilation analytic and diverge at infinity. Our approach is based on an abstract theorem related to dilation analytic methods, and our results on the Dirac operator are obtained by analyzing dilated relativistic Schrödinger operators. Moreover, we explain some relationships of spectra and resonances between Schrödinger operators and the Dirac operator as the nonrelativistic limit.


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Hiroshi T. ITO. Osanobu YAMADA. "Relativistic Hamiltonians with dilation analytic potentials diverging at infinity." J. Math. Soc. Japan 63 (4) 1311 - 1357, October, 2011.


Published: October, 2011
First available in Project Euclid: 27 October 2011

zbMATH: 1252.81060
MathSciNet: MR2855814
Digital Object Identifier: 10.2969/jmsj/06341311

Primary: 35P20
Secondary: 81Q15

Keywords: Dirac operator , nonrelativistic limit , relativistic Schrödinger operator , resonances

Rights: Copyright © 2011 Mathematical Society of Japan

Vol.63 • No. 4 • October, 2011
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