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SUMMARY:Dirac Operators with Square-Integrable Potentials - Hughes\, D (Ca
 rdiff University)
DTSTART:20120725T130000Z
DTEND:20120725T140000Z
UID:TALK39057@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We show that the absolutely continuous part of the spectral fu
 nction of the one-dimensional Dirac operator on a half-line with a constan
 t mass term and a real\, square-integrable potential is strictly increasin
 g throughout the essential spectrum $(-infty\,-1]p[1\,infty)$. The proof 
 is based on estimates for the transmission coefficient for the full-line s
 cattering problem with a truncated potential and a subsequent limiting pro
 cedure for the spectral function. Furthermore\, we show that the absolutel
 y continuous spectrum persists when an angular momentum term is added\, th
 us establishing the result for spherically symmetric Dirac operators in hi
 gher dimensions\, too.\n
LOCATION:Seminar Room 1\, Newton Institute
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