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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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
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Language:English
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boundary matrix
friedrichs extension
regular differential expression
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Wei, Guangsheng
Zettl, Anton
description 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
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subjects boundary matrix
friedrichs extension
regular differential expression
title Friedrichs extension of singular symmetric differential operators
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