|Table of Contents|

Krein Space Related to Differential Operators

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
2006年01期
Page:
122-126
Research Field:
Publishing date:
2006-02-28

Info

Title:
Krein Space Related to Differential Operators
Author(s):
GAO Yun-lan1 2 SUN Jiong1
1. Department of Mathemat ics, Inner Mongolia University, Hohhot 010021, China; 2. Department of Mathematics, Inner Mongolia Polytechnic University, Hohhot 010051, China
Keywords:
Sturm-Liouville operators complete space indefinite inner product space ( Krein space) regular resolution posit ive subspace
PACS:
O175.3
DOI:
-
Abstract:
According to the property of Sturm-Liouville operators, a complete indefinite inner product space (Krein space) associated with the operators and its regular resolution are constructed. The propert ies of its positive and maximum posit ive subspaces are discussed.

References:

[ 1] M&oller M, Zettl A. Symmetric differential operators and their Friedrichs extension [ J] . J Differential Equations, 1995, 115: 50- 69.
[ 2] Marletta M, Zettl A. The Friedrichs extension of singular differential operators [ J] . J Differential Equations, 2000, 160: 404- 421.
[ 3] Neidhardt H, Zagrevnov V A. On semibounded restrictions of sel-f adjoint operators [ J] . Integr Equ Oper Theory , 1998, 31: 489- 512.
[ 4] Wei G S, Xu Z B. Maximal accretive realizations of regular Sturm-Liouville operators [ J] . J London Math Soc, 2002, 66( 2) : 175 - 197.
[ 5] 曹之江. 常微分算子[M] . 上海: 科学技术出版社, 1987. 1- 113.
[ 6] 张恭庆, 林源渠. 泛函分析讲义( 上册) [M] . 北京: 北京大学出版社, 1987. 1- 157.
[ 7] 夏道行, 严绍宗. 线性算子谱理论? : 不定度规空间上的算子理论[M] . 北京: 科学出版社, 1987. 1- 20.
[ 8] M&o ller M, Kong Q,Wu H, et al. Indefinite Sturm-Liouville problems [ J] . Proc Royal Soc Edinburgh, 2003, 133A: 639- 652.

Memo

Memo:
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Last Update: 2006-02-28