The periodic Dirac operator is absolutely continuous

1999 ◽  
Vol 34 (4) ◽  
pp. 377-395 ◽  
Author(s):  
M. Sh. Birman ◽  
T. A. Suslina
Keyword(s):  
Dirac Operator ◽  
Absolutely Continuous ◽  
Periodic Dirac Operator

On the spectrum of the periodic Dirac operator

1981 ◽  
Vol 89 (1-2) ◽  
pp. 55-62 ◽  
Author(s):  
B. J. Harris
Keyword(s):  
Dirac Operator ◽  
Spectral Gap ◽  
Dirac Operators ◽  
Finite Multiplicity ◽  
Infinite Multiplicity ◽  
Periodic Dirac Operator

SynopsisIn an earlier paper we considered periodic Dirac operators and obtained criteria for them to be self-adjoint and for their spectra to be devoid of eigenvalues of finite multiplicity. The question of the existence of eigenvalues of infinite multiplicity was left open. In this article we obtain further criteria for self-adjointness and show that under these conditions periodic Dirac operators do not possess eigenvalues of infinite multiplicity. We also obtain a spectral gap result.

scholarly journals Absolutely continuous spectrum of Dirac systems with potentials infinite at infinity

1997 ◽  
Vol 122 (2) ◽  
pp. 377-384 ◽  
Author(s):  
KARL MICHAEL SCHMIDT
Keyword(s):  
Dirac Operator ◽  
Real Line ◽  
Absolute Continuity ◽  
Direct Proof ◽  
Absolutely Continuous Spectrum ◽  
Absolutely Continuous ◽  
One Dimensional ◽  
Dirac Systems ◽  
Positive Variation ◽  
Special Case

It is shown that the spectrum of a one-dimensional Dirac operator with a potential q tending to infinity at infinity, and such that the positive variation of 1/q is bounded, covers the whole real line and is purely absolutely continuous. An example is given to show that in general, pure absolute continuity is lost if the condition on the positive variation is dropped. The appendix contains a direct proof for the special case of subordinacy theory used.

Sign in / Sign up

Export Citation Format

Share Document