Quadratic form techniques and the Balslev-Combes theorem

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We extend the theorem of Balslev and Combes on the absence of singular continuous spectrum to a class of interactions includingr −α(3/2≦α<2) local potentials. In addition, we note that the theory of sectorial operators allows a simplification of their proof and allows one to push the cuts through angles larger than the π/2 restriction employed by Balslev-Combes.

A. Sloan Foundation Fellow.