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Weyl product algebras and modulation spaces

Holst, Anders LU ; Toft, Joachim and Wahlberg, Patrik (2007) In Journal of Functional Analysis 251(2). p.463-491
Abstract
We discuss algebraic properties of the Weyl product acting on modulation spaces. For a certain class of weight functions omega we prove that M-(omega)(p,q) is an algebra under the Weyl product if p epsilon [1, infinity] and 1 <= q <= min(p, p '). For the remaining cases P epsilon [1, infinity] and min(p, p ') < q <= infinity we show that the unweighted spaces M-p,M-q are not algebras under the Weyl product. (C) 2007 Elsevier Inc. All rights reserved.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
modulation spaces, Weyl calculus, pseudo-differential calculus, Banach, algebras
in
Journal of Functional Analysis
volume
251
issue
2
pages
463 - 491
publisher
Elsevier
external identifiers
  • wos:000250014400003
  • scopus:34548389797
ISSN
0022-1236
DOI
10.1016/j.jfa.2007.07.007
language
English
LU publication?
yes
id
cae0bd4b-9c6c-4c6c-bd64-640481e52c11 (old id 655185)
date added to LUP
2007-12-12 15:56:12
date last changed
2017-10-01 04:45:00
@article{cae0bd4b-9c6c-4c6c-bd64-640481e52c11,
  abstract     = {We discuss algebraic properties of the Weyl product acting on modulation spaces. For a certain class of weight functions omega we prove that M-(omega)(p,q) is an algebra under the Weyl product if p epsilon [1, infinity] and 1 &lt;= q &lt;= min(p, p '). For the remaining cases P epsilon [1, infinity] and min(p, p ') &lt; q &lt;= infinity we show that the unweighted spaces M-p,M-q are not algebras under the Weyl product. (C) 2007 Elsevier Inc. All rights reserved.},
  author       = {Holst, Anders and Toft, Joachim and Wahlberg, Patrik},
  issn         = {0022-1236},
  keyword      = {modulation spaces,Weyl calculus,pseudo-differential calculus,Banach,algebras},
  language     = {eng},
  number       = {2},
  pages        = {463--491},
  publisher    = {Elsevier},
  series       = {Journal of Functional Analysis},
  title        = {Weyl product algebras and modulation spaces},
  url          = {http://dx.doi.org/10.1016/j.jfa.2007.07.007},
  volume       = {251},
  year         = {2007},
}