Localization and Semibounded Energy - A Weak Unique Continuation Theorem

Details Localization and Semibounded Energy - A Weak Unique Continuation Theorem Localization and Semibounded Energy - A Weak Unique Continuation Theorem

1999-10-15

arxiv.org/abs/math-ph/9910023v1

J. Geom. Phys. 34 , 155-161 (2000)

Physics

Mathematical Physics

9 pages, 1 figure, LaTeX

Scientific paper

10.1016/S0393-0440(99)00060-1

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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