The symbols of an algebra of pseudodifferential operators

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Elmar Schrohe

Externe Organisationen

  • Johannes Gutenberg-Universität Mainz
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)211-224
Seitenumfang14
FachzeitschriftPacific journal of mathematics
Jahrgang125
Ausgabenummer1
PublikationsstatusVeröffentlicht - 1 Nov. 1986
Extern publiziertJa

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 Sachgebiete

Zitieren

The symbols of an algebra of pseudodifferential operators. / Schrohe, Elmar.
in: Pacific journal of mathematics, Jahrgang 125, Nr. 1, 01.11.1986, S. 211-224.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Schrohe E. The symbols of an algebra of pseudodifferential operators. Pacific journal of mathematics. 1986 Nov 1;125(1):211-224. doi: 10.2140/pjm.1986.125.211
Schrohe, Elmar. / The symbols of an algebra of pseudodifferential operators. in: Pacific journal of mathematics. 1986 ; Jahrgang 125, Nr. 1. S. 211-224.
Download
@article{36a98bfacf024aac967d381b5d98ad1c,
title = "The symbols of an algebra of pseudodifferential operators",
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 {\textquoteleft}symbol{\textquoteright}, 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∞.",
author = "Elmar Schrohe",
note = "Copyright: Copyright 2017 Elsevier B.V., All rights reserved.",
year = "1986",
month = nov,
day = "1",
doi = "10.2140/pjm.1986.125.211",
language = "English",
volume = "125",
pages = "211--224",
journal = "Pacific journal of mathematics",
issn = "0030-8730",
publisher = "University of California, Berkeley",
number = "1",

}

Download

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 -