ダン　ユウヤ   DAN Yuya   檀　裕也    所属   松山大学  経営学部 経営学科    職種   教授
言語種別	英語
発行・発表の年月	2014/08
形態種別	学会報告
査読	査読有り
標題	Riesz means of bound states for Schrödinger operators
執筆形態	単著
掲載誌名	SEOUL ICM 2014, International Congress of Mathematicians
出版社・発行元	SC11-03-01, Mathematical Physics
概要	The energy of ground states for quantum complex systems with the electromagnetic interaction can be determined from the spectrum calculated for the Schrödinger operator. It has been proven that the Riesz mean of all negative energies for the Hamiltonian is bounded with good coefficients. Lieb and Thirring conjectured that the coefficient in the inequalities should coincide with the semi-classical one according to the Thomas-Fermi model. Now, the refinement of the coefficients shown in 2008 by Dolbeault, Laptev and Loss is believed to be best possible. On the other hand, Rumin and Solovej showed another approach for a derivation of the Lieb-Thirring coefficient in 2011. The main result is to propose a sufficient condition for the Lieb-Thirring conjecture according to the method by Rumin-Solovej.