Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A characterization of positive self-adjoint extensions and its application to ordinary differential operators


Authors: Guangsheng Wei and Yaolin Jiang
Journal: Proc. Amer. Math. Soc. 133 (2005), 2985-2995
MSC (2000): Primary 47A20; Secondary 47E05, 34L05
Published electronically: March 22, 2005
MathSciNet review: 2159777
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A new characterization of the positive self-adjoint extensions of symmetric operators, $T_0$, is presented, which is based on the Friedrichs extension of $T_0,$ a direct sum decomposition of domain of the adjoint $T_0^{*}$ and the boundary mapping of $T_0^{*}$. In applying this result to ordinary differential equations, we characterize all positive self-adjoint extensions of symmetric regular differential operators of order $2n$ in terms of boundary conditions.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47A20, 47E05, 34L05

Retrieve articles in all journals with MSC (2000): 47A20, 47E05, 34L05


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: http://dx.doi.org/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
Published electronically: 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
Article copyright: © Copyright 2005 American Mathematical Society