Localization and semibounded energy — a weak unique continuation theorem

Aronszajn, 1957, A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second-order, J. Math. Pures Appl., 36, 235 Atiyah, 1975, Spectral asymmetry and Riemannian geometry I, Math. Proc. Cambridge Philos. Soc., 77, 43, 10.1017/S0305004100049410 Bär, 1997, On nodal sets for Dirac and Laplace operators, Commun. Math. Phys., 188, 709, 10.1007/s002200050184 C. Bär, Zero sets of solutions to semilinear elliptic systems of first-order, Invent. Math. 138 (1999) 183–202. N. Berline, E. Getzler, M. Vergne, Heat Kernels and Dirac Operators, Springer, Berlin, 1991. B. Booß-Bavnbek, Unique continuation property for Dirac operators, revisited, Preprint, Roskilde University, 1999. B. Booß-Bavnbek, K.P. Wojciechowski, Elliptic Boundary Problems for Dirac Operators, Birkhäuser, Basel, 1993. Gromov, 1983, Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Publ. Math. Inst. Hautes Etud. Sci., 58, 295 Kazdan, 1988, Unique continuation in geometry, Comm. Pure Appl. Math., 41, 667, 10.1002/cpa.3160410508 J. Roe, Elliptic Operators, Topology and Asymptotic Methods, Longman, New York, 1988. L.H. Ryder, Quantum Field Theory, 2nd ed., Cambridge University Press, Cambridge, 1996. B. Thaller, The Dirac Equation, Springer, Berlin, 1992.