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Semi‐Classical Asymptotics of Riesz Means
Author(s) -
Bruneau Vincent
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610700001265
Subject(s) - mathematics , eigenvalues and eigenvectors , conjecture , hamiltonian (control theory) , term (time) , mathematical physics , pure mathematics , mathematical analysis , physics , quantum mechanics , mathematical optimization
The semi‐classical asymptotic behaviour of the Riesz means of a distribution of eigenvalues is investigated at a non‐critical energy level. For Schrödinger type operators, the second term related to the periodic trajectories of the classical Hamiltonian is obtained. This oscillating term is explained for Riesz means of order 1 with the aim of discussing a Lieb–Thirring conjecture.