Pseudodifferential operators on manifolds with fibred boundaries
| dc.creator | Mazzeo, Rafe | |
| dc.creator | Melrose, Richard B. | |
| dc.date | 1998-12-18 | |
| dc.date.accessioned | 2026-07-07T05:27:19Z | |
| dc.date.available | 2026-07-07T05:27:19Z | |
| dc.description | Let $X$ be a compact manifold with boundary. Suppose that the boundary is fibred, $ϕ:\pa X\longrightarrow Y,$ and let $x\in\CI(X)$ be a boundary defining function. This data fixes the space of `fibred cusp' vector fields, consisting of those vector fields $V$ on $X$ satisfying $Vx=O(x^2)$ and which are tangent to the fibres of $ϕ;$ it is a Lie algebra and $\CI(X)$ module. This Lie algebra is quantized to the `small calculus' of pseudodifferential operators $\PsiF*(X).$ Mapping properties including boundedness, regularity, Fredholm condition and symbolic maps are discussed for this calculus. The spectrum of the Laplacian of an `exact fibred cusp' metric is analyzed as is the wavefront set associated to the calculus. | |
| dc.identifier | https://arxiv.org/abs/math/9812120 | |
| dc.identifier | http://arxiv.org/abs/math/9812120 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77875 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.title | Pseudodifferential operators on manifolds with fibred boundaries | |
| dc.type | text |