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Volume 9, Number 6, 2019, Pages 2190-2211                                                                DOI:10.11948/20180343
New canonical forms of self-adjoint boundary conditions for regular differential operators of order four
Qinglan Bao,Jiong Sun,Xiaoling Hao,Anton Zettl
Keywords:Differential operators, boundary conditions, self-adjoint, canonical forms.
Abstract:
      In this paper, we find new canonical forms of self-adjoint boundary conditions for regular differential operators of order two and four. In the second order case the new canonical form unifies the coupled and separated canonical forms which were known before. Our fourth order forms are similar to the new second order ones and also unify the coupled and separated forms. Canonical forms of self-adjoint boundary conditions are instrumental in the study of the dependence of eigenvalues on the boundary conditions and for their numerical computation. In the second order case this dependence is now well understood due to some surprisingly recent results given the long history and voluminous literature of Sturm-Liouville problems. And there is a robust code for their computation: SLEIGN2.
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