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2000 Mathematics Subject Classification: 35P25, 35R30, 58J50.
Using the free-space translation representation (modified Radon transform) of Lax and Phillips in odd dimensions, it is shown that the generalized backscattering transform (so outgoing angle w = Sq in terms of the incoming angle with S orthogonal and Id-S invertible) may be further restricted to give an entire, globally Fredholm, operator on appropriate Sobolev spaces of potentials with compact support. As a corollary we show...
The notion of a local line bundle on a manifold, classified by 2-cohomology with real
coefficients, is introduced. The twisting of pseudodifferential operators by such a line
bundle leads to an algebroid with elliptic elements with real-valued index, given by a
twisted variant of the Atiyah-Singer index formula. Using ideas of Boutet de Monvel and
Guillemin the corresponding twisted Toeplitz algebroid on any compact symplectic manifold
is shown to yield the star products...
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