Cwikel-Lieb-Rozenblum type inequalities for Hardy-Schrödinger operator

被引：0
|
作者：
Duong, Giao Ky [1 ,2 ]
Frank, Rupert L. [1 ,2 ,3 ]
Le, Thi Minh Thao [4 ]
Nam, Phan Thanh [1 ,2 ]
Nguyen, Phuoc-Tai [4 ]
机构：
[1] Ludwig Maximilians Univ Munchen, Dept Math, Munich, Germany
[2] Munich Ctr Quantum Sci & Technol MCQST, Munich, Germany
[3] Caltech, Dept Math, Pasadena, CA USA
[4] Masaryk Univ, Dept Math & Stat, Brno, Czech Republic
来源：
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2024年 / 190卷
基金：
美国国家科学基金会;
关键词：
Schr & ouml; dinger operator; Semiclassical estimates; Cwikel-Lieb-Rozenblum inequality; Singular potentials; THIRRING INEQUALITIES; SCHRODINGER-OPERATORS; ASYMPTOTIC-BEHAVIOR; SPECTRAL THEORY; BOUND-STATES; SOBOLEV; STABILITY; EQUATION; ENERGY; NUMBER;
D O I：
10.1016/j.matpur.2024.103598
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative eigenvalues of the Hardy-Schr & ouml;dinger operator -Delta-(d-2)(2)/(4|x|(2))-W(x) on L-2(R-d). The bound is given in terms of a weighted Ld/2-norm of W which is sharp in both large and small coupling regimes. We also obtain a similar bound for the fractional Laplacian. (c) 2024 The Author(s). Published by Elsevior Masson SAS. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
引用
收藏
页数：16
相关论文
共 50 条
12345