<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-00759367</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-15T10:46:52+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Legendre functions and the theory of characteristics</title>
            <author role="aut">
              <persName>
                <forename type="first">Jean-Paul</forename>
                <surname>Penot</surname>
              </persName>
              <email type="md5">45b92cb16978f763f73304871c128a5b</email>
              <email type="domain">ann.jussieu.fr</email>
              <idno type="idhal" notation="numeric">933439</idno>
              <idno type="halauthorid" notation="string">231103-933439</idno>
              <affiliation ref="#struct-25"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Christian</forename>
                <surname>David</surname>
              </persName>
              <email type="md5">036d679ffc444452f8ec88ed134069e8</email>
              <email type="domain">ann.jussieu.fr.invalid</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2012-11-30 15:01:02</date>
              <date type="whenWritten">2012-11-30</date>
              <date type="whenModified">2024-05-03 13:33:28</date>
              <date type="whenReleased">2012-11-30 16:21:48</date>
              <date type="whenProduced">2012-11-30</date>
              <date type="whenEndEmbargoed">2012-11-30</date>
              <ref type="file" target="https://hal.science/hal-00759367v1/document">
                <date notBefore="2012-11-30"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00759367v1/file/R12113.pdf" id="file-759367-584544">
                <date notBefore="2012-11-30"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="117538">
                <persName>
                  <forename>Christian</forename>
                  <surname>David</surname>
                </persName>
                <email type="md5">036d679ffc444452f8ec88ed134069e8</email>
                <email type="domain">ann.jussieu.fr.invalid</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00759367</idno>
            <idno type="halUri">https://hal.science/hal-00759367</idno>
            <idno type="halBibtex">penot:hal-00759367</idno>
            <idno type="halRefHtml">2012</idno>
            <idno type="halRef">2012</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-759367-584544"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-PARIS7" corresp="UNIV-PARIS">Université Denis Diderot - Paris VII</idno>
            <idno type="stamp" n="UPMC" corresp="SORBONNE-UNIVERSITE">Université Pierre et Marie Curie</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="LJLL" corresp="SORBONNE-UNIVERSITE">Laboratoire Jacques-Louis Lions</idno>
            <idno type="stamp" n="LARA">LARA</idno>
            <idno type="stamp" n="UPMC_POLE_1" corresp="UPMC">UPMC Pôle 1</idno>
            <idno type="stamp" n="SORBONNE-UNIVERSITE">Sorbonne Université</idno>
            <idno type="stamp" n="SU-SCIENCES" corresp="SORBONNE-UNIVERSITE">Faculté des Sciences de Sorbonne Université</idno>
            <idno type="stamp" n="UNIV-PARIS">Université Paris Cité</idno>
            <idno type="stamp" n="SU-TI">Sorbonne Université - Texte Intégral</idno>
            <idno type="stamp" n="ALLIANCE-SU"> Alliance Sorbonne Université</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="1">Not set</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Legendre functions and the theory of characteristics</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Jean-Paul</forename>
                    <surname>Penot</surname>
                  </persName>
                  <email type="md5">45b92cb16978f763f73304871c128a5b</email>
                  <email type="domain">ann.jussieu.fr</email>
                  <idno type="idhal" notation="numeric">933439</idno>
                  <idno type="halauthorid" notation="string">231103-933439</idno>
                  <affiliation ref="#struct-25"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Characteristics</term>
                <term xml:lang="en">Ekeland function</term>
                <term xml:lang="en">Ekeland transform</term>
                <term xml:lang="en">Hamilton-Jacobi equations</term>
                <term xml:lang="en">Legendre function</term>
                <term xml:lang="en">Legendre transform</term>
                <term xml:lang="en">Subdifferential</term>
              </keywords>
              <classCode scheme="halDomain" n="info.info-na">Computer Science [cs]/Numerical Analysis [cs.NA]</classCode>
              <classCode scheme="halTypology" n="REPORT">Reports</classCode>
              <classCode scheme="halOldTypology" n="REPORT">Reports</classCode>
              <classCode scheme="halTreeTypology" n="REPORT">Reports</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We devise a framework encompassing the classical theory of characteristics and the theory valid in the convex case recently obtained by R.T. Rockafellar and P. Wolenski. It relies on a notion of transform introduced by I. Ekeland. It involves a class of functions called Ekeland functions which is large enough to encompass convex functions, concave functions and linear-quadratic functions, as well as the class of classical Legendre functions. We also introduce a class of functions called (generalized) Legendre functions which is not as large as the class of Ekeland functions but has better reciprocity properties. It is obtained by an extension procedure and it enables one to recover the usual Fenchel-Legendre transform of convex functions.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-25" status="OLD">
          <idno type="RNSR">199712644L</idno>
          <orgName>Laboratoire Jacques-Louis Lions</orgName>
          <orgName type="acronym">LJLL</orgName>
          <desc>
            <address>
              <addrLine>Université Pierre et Marie Curie, Boîte courrier 187 - 75252 Paris Cedex 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ljll.math.upmc.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-93591" type="direct"/>
            <relation active="#struct-300301" type="direct"/>
            <relation name="UMR7598" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-93591" status="OLD">
          <idno type="ROR">https://ror.org/02en5vm52</idno>
          <orgName>Université Pierre et Marie Curie - Paris 6</orgName>
          <orgName type="acronym">UPMC</orgName>
          <date type="end">2017-12-31</date>
          <desc>
            <address>
              <addrLine>4 place Jussieu - 75005 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.upmc.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300301" status="OLD">
          <idno type="IdRef">027542084</idno>
          <idno type="ISNI">0000000121514068</idno>
          <idno type="ROR">https://ror.org/02n7qrg46</idno>
          <orgName>Université Paris Diderot - Paris 7</orgName>
          <orgName type="acronym">UPD7</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>5 rue Thomas-Mann - 75205 Paris cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-paris-diderot.fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>