The essential spectrum of N-body systems with asymptotically homogeneous order-zero interactions

Vladimir Georgescu, Victor Nistor

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1023-1027
Number of pages5
JournalComptes Rendus Mathematique
Volume352
Issue number12
DOIs
StatePublished - Dec 1 2014

Fingerprint

Essential Spectrum
Algebra
Zero
Interaction
Uniformly continuous
Cross product
Vector space
Continuous Function
Infinity
Topology
Invariant
Theorem

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Georgescu, Vladimir ; Nistor, Victor. / The essential spectrum of N-body systems with asymptotically homogeneous order-zero interactions. In: Comptes Rendus Mathematique. 2014 ; Vol. 352, No. 12. pp. 1023-1027.
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The essential spectrum of N-body systems with asymptotically homogeneous order-zero interactions. / Georgescu, Vladimir; Nistor, Victor.

In: Comptes Rendus Mathematique, Vol. 352, No. 12, 01.12.2014, p. 1023-1027.

Research output: Contribution to journalArticle

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