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Fibrations, compactifications and algebras of pseudodifferential operators

Richard B. Melrose

Respectfully dedicated to Lars Hörmander on the occasion of his sixty-fifth unbirthday


Some recent, and some new, results on the structure of algebras of pseudodifferential operators on compact manifolds with boundary are discussed. In particular their relationship to compactifications of non-compact spaces is emphasized. It is shown how these relationships allow the methods of pseudodifferential operators (``microlocalization'') to be applied to problems in scattering and spectral theory.

Richard B. Melrose
Sat Mar 30 08:04:03 EST 1996