## A Characterization of the Non-local Boundary Value Problems Associated with an Elliptic Operator |

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algebraically and topologically assumption Au,v Au)w boundary condition boundary differential operators boundary operators Boundary value problems bounded sesquilinear form C D(a closable closed operator closed subspace contained Corollary 2.1 correspond to T:V D(AQ dense in D(a dissipative operators domain elliptic operator equivalent essential spectrum extension of Aq follows formally selfadjoint Fredholm operator graphtopology Green's formula H J 2(r H^fi Hilbert space HS(fi HS(r implies integer isomorphism Lemma Let A correspond Let u e Lions-Magenes 26 lower bounded operator lower bounded sesquilinear m(AQ maximal lower bounded maximal nonnegative maximal positive Neumann condition norm nullspace numerical range operator L:X Proposition 6.1 proved regularly lower bounded regularly nonnegative regularly positive Remark represents a Neumann represents the Neumann satisfies selfadjoint operator sense of Corollary subset subspace of Z(A Theorem 2.1 theory topological sum u e D(A u,v e unique v e D(A z e D(T