<?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-00921685v1</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="2026-04-28T14:43:28+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">A dynamical system approach to Heisenberg Uniqueness Pairs</title>
            <author role="aut">
              <persName>
                <forename type="first">Philippe</forename>
                <surname>Jaming</surname>
              </persName>
              <email type="md5">73f7d82867aeff719aa1b26478f7306a</email>
              <email type="domain">math.u-bordeaux.fr</email>
              <idno type="idhal" notation="string">philippe-jaming</idno>
              <idno type="idhal" notation="numeric">2156</idno>
              <idno type="halauthorid" notation="string">15274-2156</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-8187-1534</idno>
              <idno type="IDREF">https://www.idref.fr/159701430</idno>
              <affiliation ref="#struct-27730"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Karim</forename>
                <surname>Kellay</surname>
              </persName>
              <email type="md5">91af428a397f6f7fb62e10fbd479ad63</email>
              <email type="domain">math.u-bordeaux.fr</email>
              <idno type="idhal" notation="string">karim-kellay</idno>
              <idno type="idhal" notation="numeric">997</idno>
              <idno type="halauthorid" notation="string">7400-997</idno>
              <idno type="IDREF">https://www.idref.fr/095858512</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-2529-5987</idno>
              <affiliation ref="#struct-27730"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Philippe</forename>
                <surname>Jaming</surname>
              </persName>
              <email type="md5">73f7d82867aeff719aa1b26478f7306a</email>
              <email type="domain">math.u-bordeaux.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2013-12-20 18:30:35</date>
              <date type="whenModified">2024-04-03 12:52:03</date>
              <date type="whenReleased">2013-12-21 11:59:25</date>
              <date type="whenProduced">2013-12-20</date>
              <date type="whenEndEmbargoed">2013-12-20</date>
              <ref type="file" target="https://hal.science/hal-00921685v1/document">
                <date notBefore="2013-12-20"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00921685v1/file/Heisenbergpair131219.pdf" id="file-921685-231457">
                <date notBefore="2013-12-20"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/1312.6236"/>
            </edition>
            <edition n="v2">
              <date type="whenSubmitted">2014-06-30 15:04:52</date>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="100281">
                <persName>
                  <forename>Philippe</forename>
                  <surname>Jaming</surname>
                </persName>
                <email type="md5">73f7d82867aeff719aa1b26478f7306a</email>
                <email type="domain">math.u-bordeaux.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00921685</idno>
            <idno type="halUri">https://hal.science/hal-00921685</idno>
            <idno type="halBibtex">jaming:hal-00921685</idno>
            <idno type="halRefHtml">2013</idno>
            <idno type="halRef">2013</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-921685-231457"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt/>
          <notesStmt>
            <note type="audience" n="1">Not set</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">A dynamical system approach to Heisenberg Uniqueness Pairs</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Philippe</forename>
                    <surname>Jaming</surname>
                  </persName>
                  <email type="md5">73f7d82867aeff719aa1b26478f7306a</email>
                  <email type="domain">math.u-bordeaux.fr</email>
                  <idno type="idhal" notation="string">philippe-jaming</idno>
                  <idno type="idhal" notation="numeric">2156</idno>
                  <idno type="halauthorid" notation="string">15274-2156</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-8187-1534</idno>
                  <idno type="IDREF">https://www.idref.fr/159701430</idno>
                  <affiliation ref="#struct-27730"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Karim</forename>
                    <surname>Kellay</surname>
                  </persName>
                  <email type="md5">91af428a397f6f7fb62e10fbd479ad63</email>
                  <email type="domain">math.u-bordeaux.fr</email>
                  <idno type="idhal" notation="string">karim-kellay</idno>
                  <idno type="idhal" notation="numeric">997</idno>
                  <idno type="halauthorid" notation="string">7400-997</idno>
                  <idno type="IDREF">https://www.idref.fr/095858512</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-2529-5987</idno>
                  <affiliation ref="#struct-27730"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <idno type="arxiv">1312.6236</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Uncertainty principles</term>
                <term xml:lang="en">annihilating pairs</term>
                <term xml:lang="en">Heisenberg pairs</term>
              </keywords>
              <classCode scheme="classification">42A68;42C20</classCode>
              <classCode scheme="halDomain" n="math.math-ca">Mathematics [math]/Classical Analysis and ODEs [math.CA]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Let $\Lambda$ be a set of lines in $\mathbb{R}^2$ that intersect at the origin. For $\Gamma\subset\mathbb{R}^2$ a smooth curve, we denote by $\mathcal{A}\mathcal{C}(\Gamma)$ the subset of finite measures on $\Gamma$ that are absolutely continuous with respect to arc length on $\Gamma$. For such a $\mu$, $\widehat{\mu}$ denotes the Fourier transform of $\mu$. Following Hendenmalm and Montes-Rodríguez, we will say that $(\Gamma,\Lambda)$ is a Heisenberg Uniqueness Pair if $\mu\in\mathcal{A}\mathcal{C}(\Gamma)$ is such that $\widehat{\mu}=0$ on $\Lambda$, then $\mu=0$. The aim of this paper is to provide new tools to establish this property. To do so, we will reformulate the fact that $\widehat{\mu}$ vanishes on $\Lambda$ in terms of an invariance property of $\mu$ induced by $\Lambda$. This leads us to a dynamical system on $\Gamma$ generated by $\Lambda$. The investigation of this dynamical system allows us to establish that $(\Gamma,\Lambda)$ is a Heisenberg Uniqueness Pair. This way we both unify proofs of known cases (circle, parabola, hyperbola) and obtain many new examples. This method also allows to have a better geometric intuition on why $(\Gamma,\Lambda)$ is a Heisenberg Uniqueness Pair.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-27730" status="VALID">
          <idno type="IdRef">155051342</idno>
          <idno type="ISNI">0000000123024783</idno>
          <idno type="RNSR">200711916B</idno>
          <idno type="ROR">https://ror.org/05m3r1b84</idno>
          <orgName>Institut de Mathématiques de Bordeaux</orgName>
          <orgName type="acronym">IMB</orgName>
          <date type="start">2003-01-01</date>
          <desc>
            <address>
              <addrLine>351 cours de la Libération 33405 TALENCE CEDEX</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.math.u-bordeaux.fr/IMB/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-259761" type="direct"/>
            <relation active="#struct-409745" type="direct"/>
            <relation name="UMR5251" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-259761" status="VALID">
          <idno type="IdRef">175206562</idno>
          <idno type="ROR">https://ror.org/057qpr032</idno>
          <orgName>Université de Bordeaux</orgName>
          <orgName type="acronym">UB</orgName>
          <desc>
            <address>
              <addrLine>35, place Pey Berland - 33076 Bordeaux</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.u-bordeaux.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-409745" status="VALID">
          <orgName>Institut Polytechnique de Bordeaux</orgName>
          <orgName type="acronym">Bordeaux INP</orgName>
          <desc>
            <address>
              <addrLine>Avenue des facultés33405 Talence</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.bordeaux-inp.fr/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>