NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2011, 2 (4), P. 71–77
THRESHOLD EIGENFUNCTIONS AND THRESHOLD RESONANCES
OF SOME RELATIVISTIC OPERATORS
Yoshimi Saitō – Department of Mathematics, University of Alabama at Birmingham, Birmingham, USA, Emeritus Professor, saito@math.uab.edu.
Tomio Umeda – Department of Mathematical Sciences, University of Hyogo Himeji, Japan. Professor, umeda@sci.u-hyogo.ac.jp.
We give a review of recent developments on the study of threshold eigenfunctions and threshold resonances of magnetic Dirac operators and Pauli operators. Emphasis is placed on a proof of the non-existence of threshold resonances of the magnetic Dirac operators in a concise manner.
Keywords: Dirac operators, magnetic potentials, threshold, energies, threshold resonances, threshold eigenfunctions, zero modes.
UDC 517.958
PACS 02.30.Jr, 02.30.Tb, 03.65.Pm