scholarly journals Self-adjointness and invariance of the essential spectrum for Dirac operators defined as quadratic forms

1976 ◽  
Vol 48 (3) ◽  
pp. 235-247 ◽  
Author(s):  
G. Nenciu
Keyword(s):  
Essential Spectrum ◽  
Quadratic Forms ◽  
Dirac Operators

Essential Spectrum and Exponential Decay Estimates of Solutions of Elliptic Systems of Partial Differential Equations. Applications to Schrödinger and Dirac Operators

2008 ◽  
Vol 15 (2) ◽  
pp. 333-351
Author(s):  
Vladimir S. Rabinovich ◽  
Steffen Roch
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Essential Spectrum ◽  
Exponential Decay ◽  
Elliptic Systems ◽  
Dirac Operators ◽  
Decay Estimates ◽  
Partial Differential ◽  
Limit Operators ◽  
Estimates Of Solutions

Abstract The main aim of the paper is to study relations between the location of the essential spectrum and exponential decay estimates of the eigenfunctions of systems of elliptic partial differential equations. To solve this problem, we apply the limit operators method. Applications are given to the problem of exponential decay behavior of eigenfunctions of Schrödinger and Dirac operators.

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