 To handle these operators, Atiyah, Patodi and Singer introduced global boundary conditions equivalent to attaching a cylinder to the manifold along the boundary and then restricting the domain to those sections that are square integrable along the cylinder, and also introduced the Atiyah–Patodi–Singer eta invariant.This resulted in a series of papers on spectral asymmetry, which were later unexpectedly used in theoretical physics, in particular in Witten's work on anomalies.The fundamental solutions of linear hyperbolic partial differential equations often have Petrovsky lacunas