Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non‐quasianalytic classes
Identifieur interne : 000751 ( Main/Exploration ); précédent : 000750; suivant : 000752Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non‐quasianalytic classes
Auteurs : A. A. Albanese [Italie] ; D. Jornet [Espagne] ; A. Oliaro [Italie]Source :
- Mathematische Nachrichten [ 0025-584X ] ; 2012-03.
English descriptors
- KwdEn :
Abstract
We prove the following inclusion \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty} $$ WF_* (u)\subset WF_*(Pu)\cup \Sigma , \quad u\in \mathcal {E}^\prime _\ast (\Omega ), $$ \end{document} where WF* denotes the non‐quasianalytic Beurling or Roumieu wave front set, Ω is an open subset of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {R}^n$\end{document}, P is a linear partial differential operator with suitable ultradifferentiable coefficients, and Σ is the characteristic set of P. The proof relies on some techniques developed in the study of pseudodifferential operators in the Beurling setting. Some applications are also investigated.
Url:
DOI: 10.1002/mana.201010039
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 001109
- to stream Istex, to step Curation: 000F98
- to stream Istex, to step Checkpoint: 000068
- to stream Main, to step Merge: 000769
- to stream Main, to step Curation: 000751
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non‐quasianalytic classes</title>
<author><name sortKey="Albanese, A A" sort="Albanese, A A" uniqKey="Albanese A" first="A. A." last="Albanese">A. A. Albanese</name>
</author>
<author><name sortKey="Jornet, D" sort="Jornet, D" uniqKey="Jornet D" first="D." last="Jornet">D. Jornet</name>
</author>
<author><name sortKey="Oliaro, A" sort="Oliaro, A" uniqKey="Oliaro A" first="A." last="Oliaro">A. Oliaro</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:31A1B00698B95DB79E29436E8E2611B7B2F46E70</idno>
<date when="2012" year="2012">2012</date>
<idno type="doi">10.1002/mana.201010039</idno>
<idno type="url">https://api.istex.fr/document/31A1B00698B95DB79E29436E8E2611B7B2F46E70/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">001109</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001109</idno>
<idno type="wicri:Area/Istex/Curation">000F98</idno>
<idno type="wicri:Area/Istex/Checkpoint">000068</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000068</idno>
<idno type="wicri:doubleKey">0025-584X:2012:Albanese A:wave:front:sets</idno>
<idno type="wicri:Area/Main/Merge">000769</idno>
<idno type="wicri:Area/Main/Curation">000751</idno>
<idno type="wicri:Area/Main/Exploration">000751</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non‐quasianalytic classes</title>
<author><name sortKey="Albanese, A A" sort="Albanese, A A" uniqKey="Albanese A" first="A. A." last="Albanese">A. A. Albanese</name>
<affiliation wicri:level="1"><country xml:lang="fr">Italie</country>
<wicri:regionArea>Dipartimento di Matematica “E. De Giorgi”, Università del Salento, Via Per Arnesano, P. O. Box 193, I‐73100 Lecce</wicri:regionArea>
<wicri:noRegion>I‐73100 Lecce</wicri:noRegion>
</affiliation>
<affiliation></affiliation>
</author>
<author><name sortKey="Jornet, D" sort="Jornet, D" uniqKey="Jornet D" first="D." last="Jornet">D. Jornet</name>
<affiliation wicri:level="2"><country xml:lang="fr">Espagne</country>
<wicri:regionArea>Instituto Universitario de Matemática Pura y Aplicada IUMPA‐UPV, Universidad Politécnica de Valencia, C/Camino de Vera, s/n, E‐46022 Valencia</wicri:regionArea>
<placeName><region nuts="2" type="communauté">Communauté valencienne</region>
</placeName>
</affiliation>
<affiliation></affiliation>
</author>
<author><name sortKey="Oliaro, A" sort="Oliaro, A" uniqKey="Oliaro A" first="A." last="Oliaro">A. Oliaro</name>
<affiliation wicri:level="1"><country xml:lang="fr">Italie</country>
<wicri:regionArea>Dipartimento di Matematica, Università di Torino, Via Carlo Alberto, 10, I‐10123 Torino</wicri:regionArea>
<wicri:noRegion>I‐10123 Torino</wicri:noRegion>
</affiliation>
<affiliation></affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j">Mathematische Nachrichten</title>
<title level="j" type="abbrev">Math. Nachr.</title>
<idno type="ISSN">0025-584X</idno>
<idno type="eISSN">1522-2616</idno>
<imprint><publisher>WILEY‐VCH Verlag</publisher>
<pubPlace>Germany</pubPlace>
<date type="published" when="2012-03">2012-03</date>
<biblScope unit="volume">285</biblScope>
<biblScope unit="issue">4</biblScope>
<biblScope unit="page" from="411">411</biblScope>
<biblScope unit="page" to="425">425</biblScope>
</imprint>
<idno type="ISSN">0025-584X</idno>
</series>
<idno type="istex">31A1B00698B95DB79E29436E8E2611B7B2F46E70</idno>
<idno type="DOI">10.1002/mana.201010039</idno>
<idno type="ArticleID">MANA201010039</idno>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">0025-584X</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>35A18</term>
<term>35A21</term>
<term>MSC (2010) Primary: 46F05</term>
<term>Non‐quasianalytic weight function</term>
<term>linear partial differential operators</term>
<term>propagation of singularities</term>
<term>pseudodifferential operators</term>
<term>wave front set</term>
</keywords>
</textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">We prove the following inclusion \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty} $$ WF_* (u)\subset WF_*(Pu)\cup \Sigma , \quad u\in \mathcal {E}^\prime _\ast (\Omega ), $$ \end{document} where WF* denotes the non‐quasianalytic Beurling or Roumieu wave front set, Ω is an open subset of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {R}^n$\end{document}, P is a linear partial differential operator with suitable ultradifferentiable coefficients, and Σ is the characteristic set of P. The proof relies on some techniques developed in the study of pseudodifferential operators in the Beurling setting. Some applications are also investigated.</div>
</front>
</TEI>
<affiliations><list><country><li>Espagne</li>
<li>Italie</li>
</country>
<region><li>Communauté valencienne</li>
</region>
</list>
<tree><country name="Italie"><noRegion><name sortKey="Albanese, A A" sort="Albanese, A A" uniqKey="Albanese A" first="A. A." last="Albanese">A. A. Albanese</name>
</noRegion>
<name sortKey="Oliaro, A" sort="Oliaro, A" uniqKey="Oliaro A" first="A." last="Oliaro">A. Oliaro</name>
</country>
<country name="Espagne"><region name="Communauté valencienne"><name sortKey="Jornet, D" sort="Jornet, D" uniqKey="Jornet D" first="D." last="Jornet">D. Jornet</name>
</region>
</country>
</tree>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Rhénanie/explor/UnivTrevesV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000751 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000751 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Rhénanie |area= UnivTrevesV1 |flux= Main |étape= Exploration |type= RBID |clé= ISTEX:31A1B00698B95DB79E29436E8E2611B7B2F46E70 |texte= Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non‐quasianalytic classes }}
This area was generated with Dilib version V0.6.31. |