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The symbols of an
algebra of pseudodifferential operators
Elmar Schrohe |
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Vol. 125 (1986), No. 1, 211–224
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Abstract |
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Atiyah and Singer constructed a Fréchet operator algebra 𝒫∞ by closing a set of zero order pseudodifferential operators on a compact manifold X in the topology generated by all the norms of the spaces L(Hs), s real. Each operator in 𝒫∞ has a ‘symbol’, a function in C(S∗X). Contradicting a statement of Atiyah and Singer and establishing the manifold analogue of a conjecture by H. O. Cordes, it will be shown that each function in C(S∗X) is the symbol of an operator in 𝒫∞. |
Mathematical Subject Classification 2000
Primary: 58G15
Secondary: 35S05, 47G05
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Milestones
Received: 4 December 1985
Published: 1 November 1986
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Authors |
| Elmar Schrohe | |
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