Eberhard Hopf: Difference between revisions
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{{short description|German mathematician}} |
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{{Infobox scientist |
{{Infobox scientist |
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| name = Eberhard Hopf |
| name = Eberhard Hopf |
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| image = Eberhard Hopf.jpg |
| image = Eberhard Hopf.jpg |
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| birth_date = {{birth date|1902|4| |
| birth_date = {{birth date|1902|4|4|df=y}} |
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| birth_place = [[Salzburg]], [[Austria-Hungary]] |
| birth_place = [[Salzburg]], [[Austria-Hungary]] |
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| death_date = {{death date and age|1983|7|24|1902|4|14|df=y}} |
| death_date = {{death date and age|1983|7|24|1902|4|14|df=y}} |
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| death_place = [[Bloomington, Indiana]], |
| death_place = [[Bloomington, Indiana]], United States |
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| nationality = [[Germany|German]] |
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| field = [[Mathematician]] |
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| field = [[Mathematician]] |
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| doctoral_students = [[Albert Schaeffer]] |
| doctoral_students = [[Albert Schaeffer]] |
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| known_for = [[Ergodic theory]]<br>[[Partial differential equation]]<br>[[ |
| known_for = [[Bifurcation theory]]<br>[[Differential geometry]]<br>[[Ergodic theory]]<br>[[Partial differential equation]]<br>[[Hopf bifurcation]]<br>[[Hopf decomposition]]<br>[[Hopf lemma]]<br>[[Hopf maximum principle]]<br>[[Cole–Hopf transformation]]<br>{{no wrap|[[Landau–Hopf theory of turbulence]]}}<br>[[Wiener–Hopf method]] |
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| prizes = [[Leroy P. Steele Prize]] (1981)<br>[[Josiah Willard Gibbs Lectureship|Gibbs Lecture]] (1971)<br>[[List of International Congresses of Mathematicians Plenary and Invited Speakers|ICM speaker]] (1950) |
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| ⚫ | '''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 equation]]s and [[integral equation]]s, [[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 equation]]s. |
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| ⚫ | '''Eberhard Frederich Ferdinand Hopf''' (April |
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==Biography== |
==Biography== |
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| ⚫ | In 1971, Hopf was the [[American Mathematical Society]] [[Josiah Willard Gibbs|Gibbs]] Lecturer.<ref>[https://www.ams.org/meetings/lectures/meet-gibbs-lect Josiah Willard Gibbs Lectures #42], AMS</ref> In 1981, he received the [[Leroy P. Steele Prize]] from the American Mathematical Society for seminal contributions to research. |
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== Major publications == |
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In 1930 he received a fellowship from the [[Rockefeller Foundation]] to study [[classical mechanics]] with [[George David Birkhoff|George Birkhoff]] at [[Harvard]], but his appointment was at the Harvard College Observatory. In late 1931, with the help of [[Norbert Wiener]], Hopf joined the Department of Mathematics of the [[Massachusetts Institute of Technology]], accepting the position of Assistant Professor. While at MIT, Hopf did much of his work on [[ergodic theory]]. |
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*{{cite journal|title=Elementare Bemerkungen über die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus|year=1927|jfm=53.0454.02|pages=147–152|language=de|journal=Sitzungsberichte der Preußischen Akademie der Wissenschaften, Physikalisch-Mathematische Klasse|last1=Hopf|first1=E.}} |
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*{{cite journal|title=Über den funktionalen, insbesondere den analytischen Charakter der Lösungen elliptischer Differentialgleichungen zweiter Ordnung|language=de|journal=[[Mathematische Zeitschrift]]|year=1932|volume=34|pages=194–233|zbl=0002.34003|doi=10.1007/BF01180586|url=https://eudml.org/doc/168309|jfm=57.0556.01|last1=Hopf|first1=Eberhard|s2cid=120040877 }} |
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*{{cite journal|mr=0001464|last1=Hopf|first1=Eberhard|title=Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung|language=de|journal=Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig. Mathematisch-Physische Klasse|volume=91|year=1939|pages=261–304|jfm=65.1413.02|zbl=0024.08003}} |
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*{{cite journal|mr=0039141|last1=Hopf|first1=Eberhard|title=Abzweigung einer periodischen Lösung von einer stationären eines Differentialsystems|language=de|journal=Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig. Mathematisch-Physische Klasse|volume=95|year=1943|issue=1|pages=3–22|zbl=0063.02065}} |
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*{{cite journal|mr=0030113|last1=Hopf|first1=Eberhard|zbl=0031.32901|title=A mathematical example displaying features of turbulence|journal=[[Communications on Pure and Applied Mathematics]]|volume=1|year=1948a|pages=303–322|issue=4|doi=10.1002/cpa.3160010401}} |
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*{{cite journal|mr=0023591|last1=Hopf|first1=Eberhard|zbl=0030.07901|title=Closed surfaces without conjugate points|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|volume=34|year=1948b|pages=47–51|issue=2|doi=10.1073/pnas.34.2.47|pmid=16588785 |pmc=1062913 |bibcode=1948PNAS...34...47H |doi-access=free}} |
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*{{cite journal|mr=0047234|last1=Hopf|first1=Eberhard|title=The partial differential equation {{math|''u''<sub>''t''</sub> + ''uu''<sub>''x''</sub> {{=}} μ''u''<sub>''xx''</sub>}}|zbl=0039.10403|journal=[[Communications on Pure and Applied Mathematics]]|volume=3|year=1950|pages=201–230|issue=3|doi=10.1002/cpa.3160030302}} |
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*{{cite journal|mr=0050423|last1=Hopf|first1=Eberhard|zbl=0042.10604|title=Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen|language=de|journal=[[Mathematische Nachrichten]]|volume=4|year=1951|pages=213–231|doi=10.1002/mana.3210040121|issue=1–6}} |
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*{{cite journal|mr=0050126|last1=Hopf|first1=Eberhard|title=A remark on linear elliptic differential equations of second order|zbl=0048.07802|journal=[[Proceedings of the American Mathematical Society]]|volume=3|year=1952a|pages=791–793|issue=5|doi=10.1090/S0002-9939-1952-0050126-X|doi-access=free}} |
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*{{cite journal|mr=0059119|last1=Hopf|first1=Eberhard|title=Statistical hydromechanics and functional calculus|journal=[[Indiana University Mathematics Journal|Journal of Rational Mechanics and Analysis]]|volume=1|year=1952b|pages=87–123|issue=1|doi=10.1512/iumj.1952.1.51004|zbl=0049.41704|doi-access=free}} |
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*{{cite journal|mr=0182790|last1=Hopf|first1=Eberhard|title=Generalized solutions of non-linear equations of first order|journal=[[Indiana University Mathematics Journal|Journal of Mathematics and Mechanics]]|volume=14|year=1965|pages=951–973|issue=6|jstor=24901315|zbl=0168.35101}} |
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A non-comprehensive selection of his work was published in 2002: |
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| ⚫ | *{{Cite encyclopedia | editor1-last=Morawetz | editor1-first=Cathleen S. | editor2-last=Serrin | editor2-first=James B. | editor3-last=Sinai | editor3-first=Yakov G. | title=Selected works of Eberhard Hopf with commentaries | url=https://books.google.com/books?id=8TOqgRLbpaQC | publisher=[[American Mathematical Society]] | location=Providence, RI | isbn=978-0-8218-2077-3 | mr=1985954 | year=2002|zbl=1011.01017|editor-link1=Cathleen Morawetz|editor-link2=James Serrin|editor-link3=Yakov Sinai|series=Collected Works|volume=17|s2cid=117548743}} |
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{{refend}} |
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In Cambridge Hopf worked on many mathematical and astronomical subjects. His paper ''On time average theorem in dynamics'', which appeared in the [[Proceedings of the National Academy of Sciences]], is considered by many to be the first readable paper in modern ergodic theory. His book ''Mathematical problems of radiative equilibrium'' first appeared in 1934 and was reprinted in 1964. Another important contribution from this period is the theory of [[Wiener-Hopf equation]]s, which he developed in collaboration with Norbert Wiener. By 1960, a discrete version of these equations was being extensively used in electrical engineering and geophysics, their use continuing until the present day. During this time, Hopf gained a reputation for his ability of illuminating the most complex subjects for his colleagues and even for non-specialists. Because of this talent, many discoveries and proofs of other mathematicians became easier to understand after they had been described by Hopf. |
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In 1936 Hopf received and accepted an offer of a full professorship from the [[University of Leipzig]]. Hopf, with his wife Ilse and their infant daughter Barbara, returned to Germany, which by this time was under the control of the [[Nazi Party]]. |
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The book ''Ergodentheorie'', most of which was written when Hopf was still at the Massachusetts Institute of Technology, was published in 1937. In that book, containing only 81 pages, Hopf presented a precise and elegant summary of ergodic theory. In 1939 Hopf established ergodicity of the [[geodesic flow]] on [[compact space|compact]] [[hyperbolic manifold|manifolds of constant negative curvature]]. In 1940 Hopf was on the list of the invited lecturers to the [[International Congress of Mathematicians]] to be held in [[Cambridge, Massachusetts]]. Because of the start of [[World War II]], however, the Congress was cancelled. |
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In 1942 Hopf was drafted to work in the German Aeronautical Institute. In 1944, one year before the end of World War II, Hopf was appointed to a professorship at the [[University of Munich]]. In 1947, at the behest of [[Richard Courant]] he returned to the United States, where he presented the definitive solution of [[Hurewicz|Hurewicz's]] problem.{{Citation needed|date=February 2008}}<!-- Not from MacTutot, plz, they don't know what they are talking about --> |
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On 22 February 1949 Hopf became a US citizen and joined [[Indiana University (Bloomington)|Indiana University at Bloomington]] as a Professor of Mathematics. In 1962 he was made Research Professor of Mathematics, staying in that position until his death. |
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Hopf was never forgiven by many people for his moving to Germany in 1936, where the Nazi party was in power. As a result, most of his work in ergodic theory and topology was neglected or even attributed to others in the years following the end of World War II. An example of this was the expulsion of Hopf's name from the discrete version of the Wiener–Hopf equations, which were frequently referred to as "[[Wiener filter]]". |
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==Awards and honors== |
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| ⚫ | In 1971 Hopf was the [[American Mathematical Society]] [[Josiah Willard Gibbs|Gibbs]] Lecturer.<ref>[ |
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==See also== |
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* [[Hopf alternative]] |
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* [[Hopf bifurcation]] |
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* [[Hopf–Cole transformation]] (see [[Burgers' equation]]) |
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* [[Wiener–Hopf method]] |
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== Bibliography == |
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| ⚫ | *{{ |
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==External links== |
==External links== |
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* [http://gdz.sub.uni-goettingen.de/dms/suche/?tx_goobit3_search%5Border%5D=0&tx_goobit3_search%5Blink%5D=1&tx_goobit3_search%5Bformquery%5D=Hopf%20Eberhard Online list of E. Hopf's works from Göttinger Digitalisierungszentrum] |
* [http://gdz.sub.uni-goettingen.de/dms/suche/?tx_goobit3_search%5Border%5D=0&tx_goobit3_search%5Blink%5D=1&tx_goobit3_search%5Bformquery%5D=Hopf%20Eberhard Online list of E. Hopf's works from Göttinger Digitalisierungszentrum] |
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{{Authority control}} |
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{{Persondata |
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|NAME= Hopf, Eberhard |
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|ALTERNATIVE NAMES= |
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|SHORT DESCRIPTION=German mathematician |
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|DATE OF BIRTH=April 17, 1902 |
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|PLACE OF BIRTH=[[Salzburg, Austria]] |
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|DATE OF DEATH=July 24, 1983 |
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|PLACE OF DEATH=[[Indianapolis]], [[Indiana]] |
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}} |
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{{DEFAULTSORT:Hopf, Eberhard}} |
{{DEFAULTSORT:Hopf, Eberhard}} |
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[[Category:1902 births]] |
[[Category:1902 births]] |
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[[Category:1983 deaths]] |
[[Category:1983 deaths]] |
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[[Category: |
[[Category:Scientists from Salzburg]] |
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[[Category:20th-century mathematicians]] |
[[Category:20th-century German mathematicians]] |
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[[Category:German |
[[Category:German topologists]] |
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[[Category: |
[[Category:People from Austria-Hungary]] |
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[[Category:Immigrants to Germany]] |
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[[Category:Immigrants to the United States]] |
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[[de:Eberhard Hopf]] |
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[[fr:Eberhard Hopf]] |
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[[pt:Eberhard Hopf]] |
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Latest revision as of 11:19, 18 July 2024
Eberhard Hopf | |
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 | |
| Born | 4 April 1902 |
| Died | 24 July 1983 (aged 81) Bloomington, Indiana, United States |
| Nationality | German |
| 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 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:
- 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.
