Differential-boundary operators

Krall, Allan M.

doi:10.1090/S0002-9947-1971-0271445-4

Differential-boundary operators
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Trans. Amer. Math. Soc. 154 (1971), 429-458 Request permission

Addendum: Trans. Amer. Math. Soc. 180 (1973), 505.

Abstract:

Differential-boundary systems occur naturally as adjoints for ordinary differential systems involving integral boundary conditions. In this paper such systems are generalized so that the adjoint system has the same form as the original. Interior boundary points are introduced and removed, and the integrals, used in the boundary conditions, are also removed. Selfadjoint systems are classified, and an eigenfunction expansion is derived. Finally, nonselfadjoint systems are discussed and again, an eigenfunction expansion is derived.

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