Special Issue in honor of John W. Neuberger. Electron. J. Diff. Eqns., Special Issue 02 (2023), pp. 11-39.

Friedrichs extension of singular symmetric differential operators

Qinglan Bao, Guangsheng Wei, Anton Zettl

Abstract:
For singular even order symmetric differential operators we find the matrices which determine all symmetric extensions of the minimal operator. And for each of these symmetric operators which is bounded below we find the boundary condition of its Friedrichs extension. The operators of regular problems are bounded below and thus each one has a symmetric extension and thus its symmetric extension has a Friedrichs extension.

Published March 27, 2023.
Math Subject Classifications: 34B24, 34L15, 34B08, 34L05.
Key Words: Friedrichs extension; regular differential expression; boundary matrix.
DOI: https://doi.org/10.58997/ejde.sp.02.b1

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  Qinglan Bao
School of Mathematics and Statistics
Shaanxi Normal University
Xi'an 710062, China
email: baoqinglan19@163.com
  Guangsheng Wei
School of Mathematics and Statistics
Shaanxi Normal University
Xi'an 710062, China
email: weimath@vip.sina.com
Anton Zettl
Department of Mathematical Sciences
Northern Illinois University
DeKalb, Il 60115, USA
email: zettl@msn.com

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