EIGENFUNCTION EXPANSIONS AND THE ASSOCIATED SCATTERING THEORY FOR POTENTIAL PERTURBATIONS OF THE DIRAC EQUATION

1972 ◽  
Vol 23 (1) ◽  
pp. 17-55 ◽  
Author(s):  
MARK THOMPSON
Keyword(s):  
Dirac Equation ◽  
Scattering Theory ◽  
Eigenfunction Expansions

scholarly journals Scattering theory for the Dirac equation with a non-local term

2009 ◽  
Vol 139 (4) ◽  
pp. 867-878 ◽  
Author(s):  
Shuji Machihara ◽  
Kimitoshi Tsutaya
Keyword(s):  
Dirac Equation ◽  
Initial Data ◽  
Sobolev Spaces ◽  
Scattering Theory ◽  
Scattering Problem ◽  
Small Initial Data ◽  
Non Local ◽  
Scattering Operators ◽  
Local Term

Consider a scattering problem for the Dirac equation with a non-local term including the Hartree type, say the cubic convolution term. We show the existence of scattering operators for small initial data in the subcritical and critical Sobolev spaces.

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