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A characterization of positive self-adjoint extensions and its application to ordinary differential operators
Author(s):
Guangsheng
Wei;
Yaolin
Jiang
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2985-2995.
MSC (2000):
Primary 47A20;
Secondary 47E05, 34L05
Posted:
March 22, 2005
MathSciNet review:
2159777
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Abstract:
A new characterization of the positive self-adjoint extensions of symmetric operators,  , is presented, which is based on the Friedrichs extension of  a direct sum decomposition of domain of the adjoint  and the boundary mapping of  . In applying this result to ordinary differential equations, we characterize all positive self-adjoint extensions of symmetric regular differential operators of order  in terms of boundary conditions.
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Additional Information:
Guangsheng
Wei
Affiliation:
Research Center for Applied Mathematics and Institute for Information and System Science, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
Email:
weimath@pub.xaonline.com, isystem@vip.sina.com
Yaolin
Jiang
Affiliation:
Research Center for Applied Mathematics and Institute for Information and System Science, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
Email:
yljiang@xjtu.edu.cn
DOI:
10.1090/S0002-9939-05-07837-8
PII:
S 0002-9939(05)07837-8
Keywords:
Friedrichs extension,
positive self-adjoint extension,
boundary condition
Received by editor(s):
October 30, 2003
Received by editor(s) in revised form:
May 17, 2004.
Posted:
March 22, 2005
Additional Notes:
This research was supported by the National Natural Science Foundation of P. R. China (No. 10071048).
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2005,
American Mathematical Society
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