Otto Hölder
Ludwig Otto Hölder | |
|---|---|
 Otto Hölder | |
| Born | 22 December 1859 |
| Died | 29 August 1937(aged 77) |
| Nationality | German |
| Education | University of Stuttgart University of Berlin University of Tübingen |
| Known for | Hölder condition Hölder mean Hölder summation Hölder's inequality Hölder's theorem Jordan–Hölder theorem |
| Spouse | Helene Hölder |
| Children | Ernst Hölder |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Göttingen University of Tübingen University of Leipzig |
| Doctoral advisor | Paul du Bois-Reymond[1] |
| Doctoral students | |
Ludwig Otto Hölder(December 22, 1859 – August 29, 1937) was a Germanmathematicianborn inStuttgart.[2]
Early life and education[edit]
Hölder was the youngest of three sons of professor Otto Hölder (1811–1890), and a grandson of professor Christian Gottlieb Hölder (1776–1847); his two brothers also became professors. He first studied at thePolytechnikum(which today is theUniversity of Stuttgart) and then in 1877 went toBerlinwhere he was a student ofLeopold Kronecker,Karl Weierstrass,andErnst Kummer.[2]
In 1877, he entered theUniversity of Berlinand took his doctorate from theUniversity of Tübingenin 1882. The title of his doctoral thesis was "Beiträge zur Potentialtheorie" ( "Contributions topotential theory").[1]Following this, he went to theUniversity of Leipzigbut was unable tohabilitatethere, instead earning a second doctorate and habilitation at theUniversity of Göttingen,both in 1884.
Academic career and later life[edit]
He was unable to get government approval for a faculty position in Göttingen, and instead was offered a position as extraordinary professor at Tübingen in 1889. Temporary mental incapacitation delayed his acceptance but he began working there in 1890. In 1899, he took the former chair ofSophus Lieas a full professor at the University of Leipzig. There he served as dean from 1912 to 1913, and as rector in 1918.[2]
He married Helene, the daughter of a bank director and politician, in 1899. They had two sons and two daughters. His sonErnst Hölderbecame another mathematician,[2]and his daughter Irmgard married mathematicianAurel Wintner.[3]
In 1933, Hölder signed theVow of allegiance of the Professors of the German Universities and High-Schools to Adolf Hitler and the National Socialistic State.[4]
Mathematical contributions[edit]
Holder's inequality,named for Hölder, was actuallyprovenearlier byLeonard James Rogers.It is named for a paper in which Hölder, citing Rogers, reproves it;[5]in turn, the same paper includes a proof of what is now calledJensen's inequality,with some side conditions that were later removed by Jensen.[6] Hölder is also noted for many othertheoremsincluding theJordan–Hölder theorem,the theorem stating that everylinearly ordered groupthat satisfies anArchimedean propertyisisomorphicto asubgroupof the additivegroupofreal numbers,the classification ofsimple groupsoforderup to 200, theanomalous outer automorphismsof thesymmetric groupS6,andHölder's theorem,which implies that theGamma functionsatisfies noalgebraic differential equation.Another idea related to his name is theHölder condition(or Hölder continuity), which is used in many areas ofanalysis,including the theories ofpartial differential equationsandfunction spaces.
References[edit]
- ^abcdeOtto Hölderat theMathematics Genealogy Project
- ^abcdO'Connor, John J.;Robertson, Edmund F.,"Otto Hölder",MacTutor History of Mathematics Archive,University of St Andrews
- ^Elbert, Árpád; Garay, Barnabás M. (2006), "Differential equations: Hungary, the extended first half of the 20th century", in Horváth, János (ed.),A Panorama of Hungarian Mathematics in the Twentieth Century, I,Bolyai Soc. Math. Stud., vol. 14, Springer, Berlin, pp. 245–294,doi:10.1007/978-3-540-30721-1_9,MR2547513;seep. 248
- ^Bekenntnis der Professoren an den Universitäten und Hochschulen zu Adolf Hitler und dem nationalsozialistischen Staat; überreicht vom Nationalsozialistischen Lehrerbund Deutschland-Sachsen,Dresden, 1933, p. 135
- ^Maligranda, Lech (1998), "Why Hölder's inequality should be called Rogers' inequality",Mathematical Inequalities & Applications,1(1): 69–83,doi:10.7153/mia-01-05,MR1492911
- ^Guessab, A.; Schmeisser, G. (2013), "Necessary and sufficient conditions for the validity of Jensen's inequality",Archiv der Mathematik,100(6): 561–570,doi:10.1007/s00013-013-0522-3,MR3069109,S2CID56372266,
under the additional assumption thatexists, this inequality was already obtained by Hölder in 1889
| International | |
|---|---|
| National | |
| Academics | |
| People | |
| Other | |
- Group theorists
- 19th-century German mathematicians
- 20th-century German mathematicians
- 1859 births
- 1937 deaths
- Scientists from Stuttgart
- Humboldt University of Berlin alumni
- University of Tübingen alumni
- Academic staff of Leipzig University
- University of Stuttgart alumni
- Academic staff of the University of Tübingen
- Academic staff of the University of Göttingen