Positivity properties in noncommutative convolution algebras with applications in pseudo-differential calculus
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- 作者：Toft ; Joachim
- 关键词：47B65 ; 35S05 ; 35A21 ; 47B10 ; 35A18 ; 43A35 ; 42A82 ; Positivity ; Twisted convolution ; Weyl quantization ; Pseudo-differential operators ; Bochner&ndash ; Schwartz theorem ; Schatten&ndash ; von Neumann classes
- 刊名：Bulletin des Sciences Mathematiques
- 出版年：2003
- 出版时间：March, 2003
- 年：2003
- 卷：127
- 期：2
- 页码：101-132
- 全文大小：299 K
文摘
We study S′+, of all a
D′ such that (a*σ
,)≥0 for every C∞0, where *σ denotes the twisted convolution. We prove that certain boundedness for aS′+ are completely determined of the behaviour for a at origin, for example that aS′, and that if a(0)<∞, then aL2∩L∞. We use the results in order to determine wether positive pseudo-differential operators belong to certain Schatten-casses or not.
D′ such that (a*σ,)≥0 for every C∞0, where *σ denotes the twisted convolution. We prove that certain boundedness for aS′+ are completely determined of the behaviour for a at origin, for example that aS′, and that if a(0)<∞, then aL2∩L∞. We use the results in order to determine wether positive pseudo-differential operators belong to certain Schatten-casses or not.