Lagrangian submanifolds at infinity and their parametrization

Abstract

We continue our study of tempered oscillatory integrals I ϕ (a), here investigating the link with a suitable symplectic structure at infinity, which we describe in detail.We prove adapted versions of the classical theorems, which show that tempered distributions of the type I ϕ (a) are indeed linked to suitable Lagrangians extending to infinity, that is, extending up to the boundary and in particular the corners of a compactification of T * R d to B d ×B d .In particular, we show that such Lagrangians can always be parametrized by non-homogeneous, regular phase functions, globally defined on some R d × R s .We also state how two such phase functions parametrizing the same Lagrangian may be considered equivalent up to infinity.

Locations

• Journal of Symplectic Geometry - View
• arXiv (Cornell University) - View - PDF
• Institutional Research Information System University of Turin (University of Turin) - View - PDF