A New Levinson’s Theorem for Potentials with Critical Decay

We study the low-energy asymptotics of the spectral shift function for Schrödinger operators with potentials decaying like . We prove a generalized Levinson’s theorem for this class of potentials in presence of zero eigenvalue and zero resonance.

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Bibliographische Detailangaben
Veröffentlicht in:	Annales Henri Poincaré 2012-02, Vol.13 (1), p.41-84
Hauptverfasser:	Jia, Xiaoyao, Nicoleau, François, Wang, Xue Ping
Format:	Artikel
Sprache:	eng
Schlagworte:	Classical and Quantum Gravitation Dynamical Systems and Ergodic Theory Elementary Particles Exact sciences and technology Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematical Physics Mathematics Nonlinear algebraic and transcendental equations Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Other topics in mathematical methods in physics Partial differential equations Physics Physics and Astronomy Quantum Field Theory Quantum Physics Relativity Theory Sciences and techniques of general use Spectral Theory Theoretical
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Beschreibung
Zusammenfassung:	We study the low-energy asymptotics of the spectral shift function for Schrödinger operators with potentials decaying like . We prove a generalized Levinson’s theorem for this class of potentials in presence of zero eigenvalue and zero resonance.
ISSN:	1424-0637 1424-0661
DOI:	10.1007/s00023-011-0117-0