Abstract
Given a Dirac operator P on a manifold with boundary, we discuss a particular local elliptic boundary condition for P as well as the (pseudo-differential) boundary condition of Atiyah-Patodi-Singer type. We prove that P is elliptic under either of these boundary conditions and extends to a self-adjoint operator with a discrete spectrum. Basic spectral estimates are given. In order to do so, we require purely functional analytic arguments and elementary estimates.
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