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. |  |