Friedrichs extension of singular symmetric differential operators

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 proble...

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Bibliographic Details
Published in:Electronic journal of differential equations 2023-03, Vol.Special Issues (Special Issue 02), p.11-39
Main Authors: Bao, Qinglan, Wei, Guangsheng, Zettl, Anton
Format: Article
Language:English
Subjects:
boundary matrix
friedrichs extension
regular differential expression
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Summary: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. See also https://ejde.math.txstate.edu/special/02/b1/abstr.html
ISSN:1072-6691
1072-6691
DOI:10.58997/ejde.sp.02.b1