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Eberhard Hopf

January 01, 1970

Eberhard Frederich Ferdinand Hopf (April 4, 1902 in Salzburg, Austria-Hungary – July 24, 1983 in Bloomington, Indiana, USA) was a German mathematician and astronomer, one of the founding fathers of ergodic theory and a pioneer of bifurcation theory who also made significant contributions to the subjects of partial differential equations and integral equations, fluid dynamics, and differential geometry. The Hopf maximum principle is an early result of his (1927) that is one of the most important techniques in the theory of elliptic partial differential equations.

Biography edit

Hopf was born in Salzburg, Austria-Hungary, but his scientific career was divided between Germany and the United States. He received his Ph.D. in mathematics in 1926 and his Habilitation in mathematical astronomy from the University of Berlin in 1929.

In 1971, Hopf was the American Mathematical Society Gibbs Lecturer.[1] In 1981, he received the Leroy P. Steele Prize from the American Mathematical Society for seminal contributions to research.

Major publications edit

  • Hopf, E. (1927). "Elementare Bemerkungen über die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus". Sitzungsberichte der Preußischen Akademie der Wissenschaften, Physikalisch-Mathematische Klasse (in German): 147–152. JFM 53.0454.02.
  • Hopf, Eberhard (1932). "Über den funktionalen, insbesondere den analytischen Charakter der Lösungen elliptischer Differentialgleichungen zweiter Ordnung". Mathematische Zeitschrift (in German). 34: 194–233. doi:10.1007/BF01180586. JFM 57.0556.01. S2CID 120040877. Zbl 0002.34003.
  • Hopf, Eberhard (1939). "Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung". Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig. Mathematisch-Physische Klasse (in German). 91: 261–304. JFM 65.1413.02. MR 0001464. Zbl 0024.08003.
  • Hopf, Eberhard (1943). "Abzweigung einer periodischen Lösung von einer stationären eines Differentialsystems". Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig. Mathematisch-Physische Klasse (in German). 95 (1): 3–22. MR 0039141. Zbl 0063.02065.
  • Hopf, Eberhard (1948a). "A mathematical example displaying features of turbulence". Communications on Pure and Applied Mathematics. 1 (4): 303–322. doi:10.1002/cpa.3160010401. MR 0030113. Zbl 0031.32901.
  • Hopf, Eberhard (1948b). "Closed surfaces without conjugate points". Proceedings of the National Academy of Sciences of the United States of America. 34 (2): 47–51. Bibcode:1948PNAS...34...47H. doi:10.1073/pnas.34.2.47. MR 0023591. PMC 1062913. PMID 16588785. Zbl 0030.07901.
  • Hopf, Eberhard (1950). "The partial differential equation ut + uux = μuxx". Communications on Pure and Applied Mathematics. 3 (3): 201–230. doi:10.1002/cpa.3160030302. MR 0047234. Zbl 0039.10403.
  • Hopf, Eberhard (1951). "Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen". Mathematische Nachrichten (in German). 4 (1–6): 213–231. doi:10.1002/mana.3210040121. MR 0050423. Zbl 0042.10604.
  • Hopf, Eberhard (1952a). "A remark on linear elliptic differential equations of second order". Proceedings of the American Mathematical Society. 3 (5): 791–793. doi:10.1090/S0002-9939-1952-0050126-X. MR 0050126. Zbl 0048.07802.
  • Hopf, Eberhard (1952b). "Statistical hydromechanics and functional calculus". Journal of Rational Mechanics and Analysis. 1 (1): 87–123. doi:10.1512/iumj.1952.1.51004. MR 0059119. Zbl 0049.41704.
  • Hopf, Eberhard (1965). "Generalized solutions of non-linear equations of first order". Journal of Mathematics and Mechanics. 14 (6): 951–973. JSTOR 24901315. MR 0182790. Zbl 0168.35101.

A non-comprehensive selection of his work was published in 2002:

Notes edit

  1. ^ Josiah Willard Gibbs Lectures #42, AMS

External links edit

January 01, 1970
eberhard, hopf, eberhard, frederich, ferdinand, hopf, april, 1902, salzburg, austria, hungary, july, 1983, bloomington, indiana, german, mathematician, astronomer, founding, fathers, ergodic, theory, pioneer, bifurcation, theory, also, made, significant, contr. Eberhard Frederich Ferdinand Hopf April 4 1902 in Salzburg Austria Hungary July 24 1983 in Bloomington Indiana USA was a German mathematician and astronomer one of the founding fathers of ergodic theory and a pioneer of bifurcation theory who also made significant contributions to the subjects of partial differential equations and integral equations fluid dynamics and differential geometry The Hopf maximum principle is an early result of his 1927 that is one of the most important techniques in the theory of elliptic partial differential equations Eberhard HopfBorn 1902 04 04 4 April 1902Salzburg Austria HungaryDied24 July 1983 1983 07 24 aged 81 Bloomington Indiana United StatesNationalityGermanAlma materUniversity of BerlinKnown forBifurcation theoryDifferential geometryErgodic theoryPartial differential equationHopf bifurcationHopf decompositionHopf lemmaHopf maximum principleCole Hopf transformationLandau Hopf theory of turbulence Wiener Hopf methodAwardsLeroy P Steele Prize 1981 Gibbs Lecture 1971 ICM speaker 1950 Scientific careerFieldsMathematicianInstitutionsMIT 1931 36 University of Leipzig 1936 42 University of Munich 1944 47 Indiana Univ Bloomington 1949 83 Doctoral advisorErhard SchmidtIssai SchurDoctoral studentsAlbert Schaeffer Contents 1 Biography 2 Major publications 3 Notes 4 External linksBiography editHopf was born in Salzburg Austria Hungary but his scientific career was divided between Germany and the United States He received his Ph D in mathematics in 1926 and his Habilitation in mathematical astronomy from the University of Berlin in 1929 In 1971 Hopf was the American Mathematical Society Gibbs Lecturer 1 In 1981 he received the Leroy P Steele Prize from the American Mathematical Society for seminal contributions to research Major publications editHopf E 1927 Elementare Bemerkungen uber die Losungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus Sitzungsberichte der Preussischen Akademie der Wissenschaften Physikalisch Mathematische Klasse in German 147 152 JFM 53 0454 02 Hopf Eberhard 1932 Uber den funktionalen insbesondere den analytischen Charakter der Losungen elliptischer Differentialgleichungen zweiter Ordnung Mathematische Zeitschrift in German 34 194 233 doi 10 1007 BF01180586 JFM 57 0556 01 S2CID 120040877 Zbl 0002 34003 Hopf Eberhard 1939 Statistik der geodatischen Linien in Mannigfaltigkeiten negativer Krummung Berichte uber die Verhandlungen der Sachsischen Akademie der Wissenschaften zu Leipzig Mathematisch Physische Klasse in German 91 261 304 JFM 65 1413 02 MR 0001464 Zbl 0024 08003 Hopf Eberhard 1943 Abzweigung einer periodischen Losung von einer stationaren eines Differentialsystems Berichte uber die Verhandlungen der Sachsischen Akademie der Wissenschaften zu Leipzig Mathematisch Physische Klasse in German 95 1 3 22 MR 0039141 Zbl 0063 02065 Hopf Eberhard 1948a A mathematical example displaying features of turbulence Communications on Pure and Applied Mathematics 1 4 303 322 doi 10 1002 cpa 3160010401 MR 0030113 Zbl 0031 32901 Hopf Eberhard 1948b Closed surfaces without conjugate points Proceedings of the National Academy of Sciences of the United States of America 34 2 47 51 Bibcode 1948PNAS 34 47H doi 10 1073 pnas 34 2 47 MR 0023591 PMC 1062913 PMID 16588785 Zbl 0030 07901 Hopf Eberhard 1950 The partial differential equation ut uux muxx Communications on Pure and Applied Mathematics 3 3 201 230 doi 10 1002 cpa 3160030302 MR 0047234 Zbl 0039 10403 Hopf Eberhard 1951 Uber die Anfangswertaufgabe fur die hydrodynamischen Grundgleichungen Mathematische Nachrichten in German 4 1 6 213 231 doi 10 1002 mana 3210040121 MR 0050423 Zbl 0042 10604 Hopf Eberhard 1952a A remark on linear elliptic differential equations of second order Proceedings of the American Mathematical Society 3 5 791 793 doi 10 1090 S0002 9939 1952 0050126 X MR 0050126 Zbl 0048 07802 Hopf Eberhard 1952b Statistical hydromechanics and functional calculus Journal of Rational Mechanics and Analysis 1 1 87 123 doi 10 1512 iumj 1952 1 51004 MR 0059119 Zbl 0049 41704 Hopf Eberhard 1965 Generalized solutions of non linear equations of first order Journal of Mathematics and Mechanics 14 6 951 973 JSTOR 24901315 MR 0182790 Zbl 0168 35101 A non comprehensive selection of his work was published in 2002 Morawetz Cathleen S Serrin James B Sinai Yakov G eds 2002 Selected works of Eberhard Hopf with commentaries Collected Works Vol 17 Providence RI American Mathematical Society ISBN 978 0 8218 2077 3 MR 1985954 S2CID 117548743 Zbl 1011 01017 Notes edit Josiah Willard Gibbs Lectures 42 AMSExternal links editO Connor John J Robertson Edmund F Eberhard Hopf MacTutor History of Mathematics Archive University of St Andrews Eberhard Hopf at the Mathematics Genealogy Project Online list of E Hopf s works from Gottinger Digitalisierungszentrum Retrieved from https en wikipedia org w index php title Eberhard Hopf amp oldid 1219058939, wikipedia, wiki, book, books, library,

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