** Next:** About this document

### Abstract:

The continuous spectrum, near its infimum, of the Laplacian for certain classes
of `doubly-warped' complete Riemannian metrics on the interiors of compact
manifolds with boundary is examined using geometric optics. General
conditions on the geometry of an algebra of vector fields leading to a
calculus of pseudodifferential operators are described and, once verified
in this particular case, the associated notion of wavefront set can be used to
show the existence of an absolute scattering matrix. This operator is
conjectured to be a Fourier integral operator; the confirmation of this
conjecture is discussed in the special case of a `double-zero' metric where
the fibrations are trivial.

*Richard B. Melrose *

Fri Nov 8 08:41:43 EST 1996