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Local wave-front sets of Banach and Fréchet types, and pseudo-differential operators
Turin University, Italy.
Linnaeus University, Faculty of Technology, Department of Mathematics. (Matematisk modellering)
Linnaeus University, Faculty of Technology, Department of Mathematics. (Matematisk modellering, Center för avancerade studier)ORCID iD: 0000-0003-1921-8168
2013 (English)In: Monatshefte für Mathematik (Print), ISSN 0026-9255, E-ISSN 1436-5081, Vol. 169, no 3-4, 285-316 p.Article in journal (Refereed) Published
Abstract [en]

Let ω, ω 0 be appropriate weight functions and ${\fancyscript{B}}$ be an invariant BF-space. We introduce the wave-front set ${{\rm WF}_{\mathcal{B}}(f)}$ with respect to the weighted Fourier Banach space ${\mathcal{B}=\fancyscript{F} \fancyscript{B}(\omega )}$ . We prove that the usual mapping properties for pseudo-differential operators Op t (a) with symbols a in ${S^{(\omega_0)}_{\rho, 0}}$ hold for such wave-front sets. In particular we prove ${{\rm WF}_{\mathcal C}({\rm Op}_t (a) f)\subseteq {\rm WF}_{\mathcal{B}}(f)}$ and ${{\rm WF}_{\mathcal{B}}(f) \subseteq {\rm WF} _{\mathcal C}({\rm Op}_t (a) f)\bigcup {\rm Char} (a)}$ . Here ${\mathcal{C}=\fancyscript{F} \fancyscript{B}(\omega /\omega_0)}$ and Char(a) is the set of characteristic points of a.

Place, publisher, year, edition, pages
Springer, 2013. Vol. 169, no 3-4, 285-316 p.
Keyword [en]
Wave-front, Fourier, Banach, Modulation, Micro-local
National Category
Mathematical Analysis
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-16966DOI: 10.1007/s00605-012-0392-yISI: 000314843500003OAI: oai:DiVA.org:lnu-16966DiVA: diva2:481449
Projects
Matematisk modellering
Available from: 2012-01-21 Created: 2012-01-21 Last updated: 2017-01-11Bibliographically approved

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Johansson, KarolineToft, Joachim
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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • asciidoc
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