Lieb-Thirring inequalities for higher order differential operators
数学物理
2007-05-23 v1 math.MP
谱理论
摘要
We derive Lieb-Thirring inequalities for the Riesz means of eigenvalues of order gamma >= 3/4 for fourth order Schr\"odinger operators in arbitrary dimensions. We also consider some extensions to polyharmonic operators, and to systems of such operators. For the critical case gamma = 1 - 1/2l in dimension d=1 with differential order 2l >= 4 we prove the strict inequality L^0(l,gamma,d) < L(l,gamma,d), which holds in contrast to current conjectures.
引用
@article{arxiv.math-ph/0412054,
title = {Lieb-Thirring inequalities for higher order differential operators},
author = {Clemens Förster and Jörgen Östensson},
journal= {arXiv preprint arXiv:math-ph/0412054},
year = {2007}
}
备注
18 pages, submitted to Comm. Part. Diff. Eq