2 results
Higher Order Scattering on Asymptotically Euclidean Manifolds
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- Journal:
- Canadian Journal of Mathematics / Volume 52 / Issue 5 / 01 October 2000
- Published online by Cambridge University Press:
- 20 November 2018, pp. 897-919
- Print publication:
- 01 October 2000
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We develop a scattering theory for perturbations of powers of the Laplacian on asymptotically Euclidean manifolds. The (absolute) scattering matrix is shown to be a Fourier integral operator associated to the geodesic flow at time
$\pi $ on the boundary. Furthermore, it is shown that on 
${{\mathbb{R}}^{n}}$ the asymptotics of certain short-range perturbations of 
${{\Delta }^{k}}$ can be recovered from the scattering matrix at a finite number of energies.
Second Order Operators with Non-Zero Eta Invariant
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- Journal:
- Canadian Mathematical Bulletin / Volume 35 / Issue 3 / 01 September 1992
- Published online by Cambridge University Press:
- 20 November 2018, pp. 341-353
- Print publication:
- 01 September 1992
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We give an example of an elliptic second order pseudodifferential operator with a non-zero eta invariant. The operator is constructed on homogeneous bundles over compact Lie groups and is formed by composing differential operators and an operator of class
In general it is not elliptic but in the special case of even dimensional bundles over SU(2) it is elliptic. The eta invariant is calculated in the special case and in the non elliptic case a difference eta invariant is obtained.
In general it is not elliptic but in the special case of even dimensional bundles over SU(2) it is elliptic. The eta invariant is calculated in the special case and in the non elliptic case a difference eta invariant is obtained.