Biography:Eberhard Hopf

Short description: German mathematician

Eberhard Hopf
Born	(1902-04-04)4 April 1902 Salzburg, Austria-Hungary
Died	24 July 1983(1983-07-24) (aged 81) Bloomington, Indiana, United States
Nationality	Germany
Alma mater	University of Berlin
Known for	Bifurcation theory Differential geometry Ergodic theory Partial differential equation Hopf bifurcation Hopf decomposition Hopf lemma Hopf maximum principle Cole–Hopf transformation Landau–Hopf theory of turbulence Wiener–Hopf method
Awards	Leroy P. Steele Prize (1981) Gibbs Lecture (1971) ICM speaker (1950)
Scientific career
Fields	Mathematician
Institutions	MIT (1931-36) University of Leipzig (1936-42) University of Munich (1944-47) Indiana Univ. Bloomington (1949-83)
Doctoral advisor	Erhard Schmidt Issai Schur
Doctoral students	Albert Schaeffer

Eberhard Frederich Ferdinand Hopf (April 4, 1902 in Salzburg, Austria-Hungary – July 24, 1983 in Bloomington, Indiana, USA) was a 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

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. In 1981, he received the Leroy P. Steele Prize from the American Mathematical Society for seminal contributions to research.

Major publications

• Hopf, E. (1927). "Elementare Bemerkungen über die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus" (in de). Sitzungsberichte der Preußischen Akademie der Wissenschaften, Physikalisch-Mathematische Klasse: 147–152. 
• Hopf, Eberhard (1932). "Über den funktionalen, insbesondere den analytischen Charakter der Lösungen elliptischer Differentialgleichungen zweiter Ordnung" (in de). Mathematische Zeitschrift 34: 194–233. doi:10.1007/BF01180586. https://eudml.org/doc/168309. 
• Hopf, Eberhard (1939). "Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung" (in de). Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig. Mathematisch-Physische Klasse 91: 261–304. 
• Hopf, Eberhard (1943). "Abzweigung einer periodischen Lösung von einer stationären eines Differentialsystems" (in de). Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig. Mathematisch-Physische Klasse 95 (1): 3–22. 
• 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. 
• 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. doi:10.1073/pnas.34.2.47. PMID 16588785. Bibcode: 1948PNAS...34...47H. 
• Hopf, Eberhard (1950). "The partial differential equation u_t + uu_x = μu_xx". Communications on Pure and Applied Mathematics 3 (3): 201–230. doi:10.1002/cpa.3160030302. 
• Hopf, Eberhard (1951). "Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen" (in de). Mathematische Nachrichten 4 (1–6): 213–231. doi:10.1002/mana.3210040121. 
• 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. 
• 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. 
• Hopf, Eberhard (1965). "Generalized solutions of non-linear equations of first order". Journal of Mathematics and Mechanics 14 (6): 951–973. 

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". Selected works of Eberhard Hopf with commentaries. Collected Works. 17. Providence, RI: American Mathematical Society. ISBN 978-0-8218-2077-3. https://books.google.com/books?id=8TOqgRLbpaQC. 

External links

• O'Connor, John J.; Robertson, Edmund F., "Eberhard Hopf", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Hopf_Eberhard.html .
• Eberhard Hopf at the Mathematics Genealogy Project
• Online list of E. Hopf's works from Göttinger Digitalisierungszentrum