The essential spectrum of N-body systems with asymptotically homogeneous order-zero interactions |
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Institution: | 1. Département de mathématiques, Université de Cergy-Pontoise, 95000 Cergy-Pontoise, France;2. Université de Lorraine, UFR MIM, île du Saulcy, CS 50128, 57045 Metz cedex 01, France;3. Pennsylvania State University, Mathematics Department, University Park, PA 16802, USA |
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Abstract: | We study the essential spectrum of N-body Hamiltonians with potentials defined by functions that have radial limits at infinity. The results extend the HVZ theorem which describes the essential spectrum of usual N-body Hamiltonians. The proof is based on a careful study of algebras generated by potentials and their cross-products. We also describe the topology on the spectrum of these algebras, thus extending to our setting a result of A. Mageira. Our techniques apply to more general classes of potentials associated with translation invariant algebras of bounded uniformly continuous functions on a finite-dimensional vector space X. |
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