Details
| Original language | English |
|---|---|
| Pages (from-to) | 211-224 |
| Number of pages | 14 |
| Journal | Pacific journal of mathematics |
| Volume | 125 |
| Issue number | 1 |
| Publication status | Published - 1 Nov 1986 |
| Externally published | Yes |
Abstract
Atiyah and Singer constructed a Frechet 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∞.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Pacific journal of mathematics, Vol. 125, No. 1, 01.11.1986, p. 211-224.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The symbols of an algebra of pseudodifferential operators
AU - Schrohe, Elmar
N1 - Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 1986/11/1
Y1 - 1986/11/1
N2 - Atiyah and Singer constructed a Frechet 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∞.
AB - Atiyah and Singer constructed a Frechet 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∞.
UR - http://www.scopus.com/inward/record.url?scp=84972556044&partnerID=8YFLogxK
U2 - 10.2140/pjm.1986.125.211
DO - 10.2140/pjm.1986.125.211
M3 - Article
AN - SCOPUS:84972556044
VL - 125
SP - 211
EP - 224
JO - Pacific journal of mathematics
JF - Pacific journal of mathematics
SN - 0030-8730
IS - 1
ER -