Localization and Semibounded Energy - A Weak Unique Continuation Theorem

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.

9 pages, 1 figure, LaTeX

References in corpus (2)

• On nodal sets for Dirac and Laplace operators
• Zero Sets of Solutions to Semilinear Elliptic Systems of First Order

Cited by in corpus (1)

• Incompatibility of Frequency Splitting and Spatial Localization: A Quantitative Analysis of Hegerfeldt's Theorem