Vol. 29, No. 1, 1969

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Boundary value problems with interior point boundary conditions

Allan Morton Krall

Vol. 29 (1969), No. 1, 161–166

Recently Neuberger, Zettl and Loud have revived interest in self-adjoint boundary value problems with interior point boundary conditions. All three have derived their results from rather extensive study of the Green’s function associated with the nonhomogeneous problem. They require G(x,ξ) = G(ξ,x).

Rather than approach the problem via the Green’s function, this article considers the problem as that of a differential operator in a Hilbert space, derives the adjoint operator, whose domain specifies the adjoint boundary conditions, and then produces necessary and sufficient conditions for self-adjointness.

Mathematical Subject Classification
Primary: 34.36
Received: 3 June 1968
Published: 1 April 1969
Allan Morton Krall