Vol. 85, No. 2, 1979

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Notes on generalized boundary value problems in Banach spaces. I. Adjoint and extension theory

Richard Clark Brown

Vol. 85 (1979), No. 2, 295–322

Let A : X Y be a densely defined closed operator where X and Y are Banach spaces. Let F be a locally convex topological vector space and H : X F an operator such that N(H) and D(A) have nontrivial intersection and D(H) is total over F. We compute AH and AH where AH is the operator determined by A on N(H) and AH(x) = (Ax,Hx)t.

We also characterize certain closed extensions of AH and the adjoints of these extensions. In particular application is made to the problem of determining self-adjoint extensions of symmetric operators restricted by boundary conditions in a Hilbert space.

Mathematical Subject Classification 2000
Primary: 47A05
Secondary: 34G10
Received: 31 July 1978
Published: 1 December 1979
Richard Clark Brown