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arXiv · math-ph/9910023

Localization and Semibounded Energy - A Weak Unique Continuation Theorem

Christian Baer
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Abstract

Let D be a self-adjoint differential operator of Dirac type acting on sections in a vector bundle over a closed Riemannian manifold M. Let H be a closed D-invariant subspace of the Hilbert space of square integrable sections. Suppose D restricted to H is semibounded. We show that every element u in H has the weak unique continuation property, i.e. if u vanishes on a nonempty open subset of M, then it vanishes on all of M.

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Christian Baer. 1999-10-15. Localization and Semibounded Energy - A Weak Unique Continuation Theorem. https://doi.org/10.1016/s0393-0440(99)00060-1

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