Absolute Continuity of Hamiltonian Operators with Repulsive Potentials

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for some positive constants a and e, then H= — A + V is absolutely continuous for 7i = l, 3. Our aim is to extend his results in two directions: One is to remove the restriction on the dimension n of the space, and the other is to remove the assumption (2). This will be accomplished except for the cases n = l and 2, where we must impose an assumption somewhat weaker than (2). Our method is that of Lavine []3] which is based on an abstract theory of Putnam ^4] on commutators of pairs of selfadjoint operators.

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