Abstract
In this paper, we develop the eigenfunction expansion theory of a selfadjoint operator generated by a symmetric sixth order differential equation L6(y)=λy. This differential equation has regular singular points at x=1, and is in the limit-5 case at each end. This means that two boundary conditions are needed at ±1 to ensure a well-posed boundary value problem. Not many examples are known of such higher order singular differential equations. The example that we give is interesting because the eigenvalue problem L6(y)=λy has a sequence of polynomial solutions that are orthogonal on [−1,1] with respect to the weight distribution W(x)=1/Aδ(x+1)+1/Bδ(x−1)+C.
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© 1982 Springer-Verlag
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Littlejohn, L.L., Krall, A.M. (1982). A singular sixth order differential equation with orthogonal polynomial eigenfunctions. In: Everitt, W., Sleeman, B. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 964. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065015
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DOI: https://doi.org/10.1007/BFb0065015
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