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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:
      We find new canonical forms of self-adjoint boundary conditions of order two and four.In the second order case the new canonical form unifies the couped and separated canonical forms which were known before. Our fourth order form is similar to the new second order one. Canonical forms are instrumental in the study of the continuous 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.