Otto Hölder

Ludwig Otto Hölder
Ludwig Otto Hölder
	Otto Hölder
Born	22 December 1859; Stuttgart, Kingdom of Württemberg
Died	29 August 1937 (aged 77); Leipzig, Germany
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
Doctoral students	Emil Artin; William Threlfall; Hermann Vermeil;

Ludwig Otto Hölder (December 22, 1859 – August 29, 1937) was a German mathematician born in Stuttgart.^[2]

Early life and education

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 the Polytechnikum (which today is the University of Stuttgart) and then in 1877 went to Berlin where he was a student of Leopold Kronecker, Karl Weierstrass, and Ernst Kummer.^[2]

In 1877, he entered the University of Berlin and took his doctorate from the University of Tübingen in 1882. The title of his doctoral thesis was "Beiträge zur Potentialtheorie" ("Contributions to potential theory").^[1] Following this, he went to the University of Leipzig but was unable to habilitate there, instead earning a second doctorate and habilitation at the University of Göttingen, both in 1884.

Academic career and later life

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 of Sophus Lie as 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 son Ernst Hölder became another mathematician,^[2] and his daughter Irmgard married mathematician Aurel Wintner.^[3]

In 1933, Hölder signed the Vow of allegiance of the Professors of the German Universities and High-Schools to Adolf Hitler and the National Socialistic State.^[4]

Mathematical contributions

Holder's inequality, named for Hölder, was actually proven earlier by Leonard 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 called Jensen's inequality, with some side conditions that were later removed by Jensen.^[6] Hölder is also noted for many other theorems including the Jordan–Hölder theorem, the theorem stating that every linearly ordered group that satisfies an Archimedean property is isomorphic to a subgroup of the additive group of real numbers, the classification of simple groups of order up to 200, the anomalous outer automorphisms of the symmetric group S₆, and Hölder's theorem, which implies that the Gamma function satisfies no algebraic differential equation. Another idea related to his name is the Hölder condition (or Hölder continuity), which is used in many areas of analysis, including the theories of partial differential equations and function spaces.

References

^ ^a ^b ^c ^d ^e Otto Hölder at the Mathematics Genealogy Project
^ ^a ^b ^c ^d O'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, ISBN 978-3-540-28945-6, MR 2547513; see p. 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, MR 1492911
^ 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, MR 3069109, S2CID 56372266, under the additional assumption that $\varphi ''$ exists, this inequality was already obtained by Hölder in 1889

[mg-1] Otto Hölder at the Mathematics Genealogy Project

[mactutor-2] O'Connor, John J.; Robertson, Edmund F., "Otto Hölder", MacTutor History of Mathematics Archive, University of St Andrews

[3] 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, ISBN 978-3-540-28945-6, MR 2547513; see p. 248

[4] 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

[5] 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, MR 1492911

[6] 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, MR 3069109, S2CID 56372266, under the additional assumption that $\varphi ''$ exists, this inequality was already obtained by Hölder in 1889

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