A SIMPLE PROOF OF THE GENERALIZED LIEB-THIRRING INEQUALITIES IN ONE-SPACE DIMENSION

被引：20

作者：

EDEN, A ^{[1
]}

FOIAS, C ^{[1
]}

机构：

[1] INDIANA UNIV,DEPT MATH,BLOOMINGTON,IN 47405

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 1991年 / 162卷 / 01期

关键词：

D O I：

10.1016/0022-247X(91)90191-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Lieb-Thirring inequalities give a sharp upper bound for the Lp-norm of a function which is the pointwise sum of the squares of a finite orthonormal sequence of functions that are elements of a suitable Sobolev space [LT]. Originally proven for the functions defined on the whole n-dimensional Euclidean space, they were later extended to bounded domains and to suborthogonal sequences of functions [GMT]. Here, we present a simple proof of these inequalities for bounded intervals in one space dimension utilizing simple Sobolev inequalities and standard results from Hilbert space theory. © 1991.

引用

页码：250 / 254

页数：5