Some problems in the spectral theory of separated Dirac operators
by Eggenberger, Joshua T., Ph.D., NORTHERN ILLINOIS UNIVERSITY, 2010, 65 pages; 3419350

Abstract:

The spectral function associated with the separated Dirac operator is investigated. Conditions under which an absolutely continuous spectrum exists are given. A connection is made between the Dirac system and a Riccati equation, and this connection is used to construct a representation of the derivative of the spectral function using a series solution of the Riccati equation. Conditions under which this series converges are given. The terms of the series are then differentiated and a representation of the second derivative of the spectral function is constructed. The question of relative asymptotic sizes of the terms of this representation are addressed.
 
AdviserBernard J. Harris
SchoolNORTHERN ILLINOIS UNIVERSITY
SourceDAI/B 71-10, p. , Oct 2010
Source TypeDissertation
SubjectsMathematics
Publication Number3419350
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