A Weak Unique Continuation Theorem

  title={A Weak Unique Continuation Theorem},
  author={Christian B{\"a}r},
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 ψ ∈ H has the weak unique continuation property, i.e. if ψ vanishes on a nonempty open subset of M , then it vanishes on all of M . 1991 Mathematics Subject Classification: 58G03, 35B05 

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