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Continuity properties in non-commutative convolution algebras, with applications in pseudo-differential calculus
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2002 (English)In: Bulletin des Sciences Mathématiques, ISSN 0007-4497, Vol. 126, no 2, 115-142 p.Article in journal (Refereed) Published
Abstract [en]

We study continuity properties for a family {s(p)} p greater than or equal to 1 of increasing Banach algebras under the twisted convolution, which also satisfies that a is an element of s(p), if and only if the Weyl operator a(w) (x, D) is a Schatten-von Neumann operator of order p on L-2. We discuss inclusion relations between the s(p)-spaces, Besov spaces and Sobolev spaces. We prove also a Young type result on sp for dilated convolution. As an application we prove that f (a) is an element of s(1), when a is an element of s(1) and f is an entire odd function. We finally apply the results on Toeplitz operators and prove that we may extend the definition for such operators. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

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PARIS: GAUTHIER-VILLARS/EDITIONS ELSEVIER , 2002. Vol. 126, no 2, 115-142 p.
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URN: urn:nbn:se:bth-8190DOI: 10.1016/S0007-4497(01)01089-2ISI: 000174392700003Local ID: diva2:835879
Available from: 2012-09-18 Created: 2009-05-08 Last updated: 2015-06-30Bibliographically approved

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