Spectral invariants for non-compactly supported Hamiltonians on the disc, and an application to the mean action spectrum

Abstract

For a symplectic isotopy on the two-dimensional disc we show that the classical spectral invariants of Viterbo [20] can be extended in a meaningful way to {\it non-compactly} supported Hamiltonians. We establish some basic properties of these extended invariants and as an application we show that Hutchings' inequality in [8] between the Calabi invariant and the mean action spectrum holds without any assumptions on the isotopy; in [8] it is assumed that the Calabi invariant is less than the rotation number (or action) on the boundary.