Weyl product algebras and modulation spaces

Anders Holst; Joachim Toft; Patrik Wahlberg

doi:10.1016/j.jfa.2007.07.007

Weyl product algebras and modulation spaces

Anders Holst, Joachim Toft, Patrik Wahlberg

Mathematics (Faculty of Engineering)

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	463-491
Journal	Journal of Functional Analysis
Volume	251
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2007.07.007
Publication status	Published - 2007

Subject classification (UKÄ)

Mathematics

Free keywords

modulation spaces
Weyl calculus
pseudo-differential calculus
Banach
algebras

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10.1016/j.jfa.2007.07.007

Cite this

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title = "Weyl product algebras and modulation spaces",

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 = "Anders Holst and Joachim Toft and Patrik Wahlberg",

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journal = "Journal of Functional Analysis",

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T1 - Weyl product algebras and modulation spaces

AU - Holst, Anders

AU - Toft, Joachim

AU - Wahlberg, Patrik

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - modulation spaces

KW - Weyl calculus

KW - pseudo-differential calculus

KW - Banach

KW - algebras

U2 - 10.1016/j.jfa.2007.07.007

DO - 10.1016/j.jfa.2007.07.007

M3 - Article

SN - 0022-1236

VL - 251

SP - 463

EP - 491

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Weyl product algebras and modulation spaces

Abstract

Subject classification (UKÄ)

Free keywords

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