# Localization and Semibounded Energy - A Weak Unique Continuation Theorem

#### Autoren: Christian Bär (2000)

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.

Zeitschrift:
J. Geom. Phys.
Verlag:
Elsevier
Seiten:
155-161
Band:
34, no. 2

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