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<title>Paul Chernoff</title>

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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Paul Chernoff</span></h1>

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<p><b>Paul Robert Chernoff</b> (* <a href="21._Juni" title="21. Juni">21. Juni</a> <a href="1942" title="1942">1942</a> in <a href="Philadelphia" title="Philadelphia">Philadelphia</a>; † <a href="17._Januar" title="17. Januar">17. Januar</a> <a href="2017" title="2017">2017</a>)<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> war ein US-amerikanischer <a href="Mathematiker" title="Mathematiker">Mathematiker</a>.

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<div class="mw-heading mw-heading2"><h2 id="Werdegang">Werdegang</h2></div>

<p>Chernoff besuchte die Central High School in Philadelphia und studierte an der <a href="Harvard_University" title="Harvard University">Harvard University</a> mit dem Bachelor-Abschluss <i>summa cum laude</i> 1963, dem Master-Abschluss 1965 und der Promotion bei <a href="George_Mackey" title="George Mackey">George Mackey</a> 1968 (<i>Semigroup Product Formulas and Addition of Unbounded Operators</i>).<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Er wurde 1969 <a href="Lecturer" title="Lecturer">Lecturer</a> in Berkeley, 1971 Assistant Professor und 1980 Professor.

</p><p>1986 war er Gastprofessor an der <a href="University_of_Pennsylvania" title="University of Pennsylvania">University of Pennsylvania</a>.

</p><p>Er befasste sich mit Funktionalanalysis (Operatortheorie) und speziell mathematischen Aspekten der Grundlagen der Quantenmechanik.

</p><p>Er war Fellow der <a href="American_Association_for_the_Advancement_of_Science" title="American Association for the Advancement of Science">American Association for the Advancement of Science</a> und der <a href="American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a>.

</p><p>Ein von ihm 1968 bewiesener Satz über Produktformeln von Halbgruppen von Operatoren unterstützt die <a href="Richard_Feynman" title="Richard Feynman">Feynmansche</a> <a href="Pfadintegral" title="Pfadintegral">Pfadintegral</a>-Formulierung der Quantenmechanik von mathematischer Seite.

</p><p>Er gab auch 1981<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> einen einfachen Beweis des Satzes von Groenewold und <a href="L%C3%A9on_Van_Hove" title="Léon Van Hove">van Hove</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Dieser betrifft die von <a href="Paul_Dirac" title="Paul Dirac">Paul Dirac</a> gefundene Korrespondenz von klassischer und Quantenmechanik, bei der Poissonklammern durch Kommutatoren von Operatoren ersetzt werden (was für Polynome in den Variablen mit Grad kleiner gleich 2 durchgeführt wird). Der Satz von Groenewold und van Hove besagt, dass das nicht auf eine Poisson-Unteralgebra der Algebra der Polynome erweitert werden kann, die alle Polynome vom Grad kleiner gleich 2 enthält (das heißt es gibt keine Erweiterung der Diracschen Quantisierungsmethode auf Polynome höheren als zweiten Grades).

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<div class="mw-heading mw-heading2"><h2 id="Schriften">Schriften</h2></div>

<ul><li><i>Note on product formulas for operator semigroups.</i> In: <i>Journal of Functional Analysis.</i> Band 2, Nr. 2, 1968, S. 238–242, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1016/0022-1236%2868%2990020-7">10.1016/0022-1236(68)90020-7</a></span>.</li>

<li><i>Essential self-adjointness of powers of generators of hyperbolic equations.</i> In: <i>Journal of Functional Analysis.</i> Band 12, Nr. 4, 1973, S. 401–414, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1016/0022-1236%2873%2990003-7">10.1016/0022-1236(73)90003-7</a></span>.</li>

<li>mit <a href="Jerrold_E._Marsden" class="mw-redirect" title="Jerrold E. Marsden">Jerrold E. Marsden</a>: <i>Properties of infinite dimensional Hamiltonian systems</i> (= <i><a href="Lecture_Notes_in_Mathematics" title="Lecture Notes in Mathematics">Lecture Notes in Mathematics</a>.</i> 425). Springer, Berlin u. a. 1974, ISBN 3-540-07011-7.</li>

<li><i>The quantum <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}">

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<annotation encoding="application/x-tex">{\displaystyle n}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a601995d55609f2d9f5e233e36fbe9ea26011b3b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" loading="lazy"></span>-body problem and a theorem of Littlewood.</i> In: <i>Pacific Journal of Mathematics.</i> Band 70, Nr. 1, 1977, S. 117–123, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.2140/pjm.1977.70.117">10.2140/pjm.1977.70.117</a></span>.</li>

<li><i>Irreducible representations of infinite-dimensional transformation groups and Lie algebras, I.</i> In: <i>Journal of Functional Analysis.</i> Band 130, Nr. 2, 1995, S. 255–282, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1006/jfan.1995.1069">10.1006/jfan.1995.1069</a></span>.</li>

<li>mit <a href="Rhonda_Hughes" title="Rhonda Hughes">Rhonda J. Hughes</a>: <i>Some examples related to Kato’s conjecture.</i> In: <i>Journal of the Australian Mathematical Society.</i> Serie A, Band 60, Nr. 2, 1996, S. 274–286, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1017/S1446788700037666">10.1017/S1446788700037666</a></span>.</li>

<li><i>Quantization and irreducible representations of infinite-dimensional transformation groups and Lie algebras.</i> In: <i>Proceedings of Mathematical Physics and Quantum Field Theory, a Symposium celebrating the Seventieth Birthday of Eyvind H. Wichmann. University of California, Berkeley, June 11–13, 1999</i> (= <i>Electronic Journal of Differential Equations, Conference.</i> 4). Southwest Texas State University, San Marcos TX 2000, S. 17–22, (<a rel="nofollow" class="external text" href="https://www.emis.de//journals/EJDE/conf-proc/04/c2/abstr.html">online</a>).</li>

<li><i>A pseudo zeta function and the distribution of primes.</i> In: <i><a href="Proceedings_of_the_National_Academy_of_Sciences_of_the_United_States_of_America" title="Proceedings of the National Academy of Sciences of the United States of America">Proceedings of the National Academy of Sciences of the United States of America</a>.</i> Band 97, Nr. 14, 2000, S. 7697–7699, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1073/pnas.97.14.7697">10.1073/pnas.97.14.7697</a></span>.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Weblinks">Weblinks</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://math.berkeley.edu/about/history/in-memoriam">In Memoriam, Universität Berkeley</a></li>

<li><a rel="nofollow" class="external text" href="https://zbmath.org/authors/chernoff.paul-r">Paul. R. Chernoff</a> in der Datenbank <a href="ZbMATH" title="ZbMATH">zbMATH</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Einzelnachweise">Einzelnachweise</h2></div>

<li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Geburts- und Karrieredaten nach <i>American Men and Women of Science</i>, Thomson Gale 2004</span>

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<li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=30697">Paul Chernoff</a> im <a href="Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a> (englisch) <span style="display:none">Vorlage:MathGenealogyProject/Wartung/id verwendet</span></span>

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<li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Chernoff: <i>Mathematical obstructions to quantization.</i> In: <i>Proceedings of the Third Workshop on Lie-admissible formulations, held at the New Harbour Campus of the University of Massachusetts in Boston from August 4 to 9, 1980</i> (= <i>Hadronic Journal.</i> Band 4, Nr. 2/4, 1981). Hadronic Press, Nonantum MA 1981, S. 879–898.</span>

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<li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">Dargestellt in <a href="Victor_Guillemin" title="Victor Guillemin">Victor Guillemin</a>, <a href="Shlomo_Sternberg" title="Shlomo Sternberg">Shlomo Sternberg</a>: <i>Symplectic Techniques in Physics.</i> Reprinted with corrections. Cambridge University Press, Cambridge u. a. 1990, ISBN 0-521-38990-9, S. 101.</span>

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<li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><a href="Rolf_Berndt_(Mathematiker)" title="Rolf Berndt (Mathematiker)">Rolf Berndt</a>: <i>Einführung in die Symplektische Geometrie.</i> Vieweg, Braunschweig u. a. 1998, ISBN 3-528-03102-6, S. 119.</span>

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Normdaten (Person): <a href="Gemeinsame_Normdatei" title="Gemeinsame Normdatei">GND</a>: <span class="-print"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/1014348358">1014348358</a></span> | <a href="Library_of_Congress_Control_Number" title="Library of Congress Control Number">LCCN</a>: <span class="-print"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n81032930">n81032930</a></span> | <a href="Virtual_International_Authority_File" title="Virtual International Authority File">VIAF</a>: <span class="-print"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/52234255/">52234255</a></span> | </div>

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