In this chapter, we will examine a number of theorems about operators H which follow from the Mourre estimate, an estimate which says that a commutator [H, iA] is positive in some sense. The ideas in this chapter can be traced back to Putnam , Kato  and Lavine  for theorems on the absence of singular spectrum, and to Weidmann  and Kalf  for theorems on absence of positive eigenvalues.
KeywordsMagnetic Field Information Technology Recent Result Quantum Information General Direction
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