Abstract
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.
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Simon, B. Quadratic form techniques and the Balslev-Combes theorem. Commun.Math. Phys. 27, 1–9 (1972). https://doi.org/10.1007/BF01649654
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DOI: https://doi.org/10.1007/BF01649654