Albert Pfluger (13 October 1907,

Oensingen Oensingen is a municipality in the district of Gäu in the canton of Solothurn in Switzerland. History Oensingen is first mentioned in 968 as ''Oingesingin cum ecclesia''. Geography Oensingen has an area, , of . Of this area, or 39.7% is us ...

– 14 September 1993, Zürich) was a Swiss mathematician, specializing in

complex function theory Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

Biography

Pfluger, the son of a farmer, attended secondary school in

Stans Stans () is the capital of the canton of Nidwalden (Nidwald) in Switzerland. The official language of Stans is German (spoken there in the variety of Swiss Standard German), but the main language is the local variant of Alemannic Swiss German. ...

. He then studied mathematics at

ETH Zürich (colloquially) , former_name = eidgenössische polytechnische Schule , image = ETHZ.JPG , image_size = , established = , type = Public , budget = CHF 1.896 billion (2021) , rector = Günther Dissertori , president = Joël Mesot , a ...

, where in 1935 he received his promotion (Ph.D) under

George Pólya George Pólya (; hu, Pólya György, ; December 13, 1887 – September 7, 1985) was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamenta ...

with thesis ''Über eine Interpretation gewisser Konvergenz- und Fortsetzungseigenschaften Dirichlet’scher Reihen''. Afterwards, he became a ''Gymnasium'' teacher at the canton school in

Zug , neighboring_municipalities = Cham, Baar, Walchwil, Steinhausen, Unterägeri , twintowns = Fürstenfeld (Austria), Kalesija (Bosnia-Herzegowina) Zug (Standard German: , Alemannic German: ; french: Zoug it, Zugo r ...

and the canton school in

Solothurn Solothurn ( , ; french: Soleure ; it, Soletta ; rm, ) is a town, a municipality, and the capital of the canton of Solothurn in Switzerland. It is located in the north-west of Switzerland on the banks of the Aare and on the foot of the Weissens ...

. He received his habilitation qualification in 1938 and in 1939 became a professor extraordinarius for applied mathematics and mathematical physics at the

University of Fribourg The University of Fribourg (french: Université de Fribourg; german: Universität Freiburg) is a public university located in Fribourg, Switzerland. The roots of the university can be traced back to 1580, when the notable Jesuit Peter Canisi ...

. At ETH Zürich he became a professor extraordinarius in 1940 and in 1943 a professor ordinarius in the professorial chair vacated by George Pólya in 1940. Pfluger retired from ETH Zürich in 1978 as professor emeritus. He did research on the value distribution theory of

Rolf Nevanlinna Rolf Herman Nevanlinna (né Neovius; 22 October 1895 – 28 May 1980) was a Finnish mathematician who made significant contributions to complex analysis. Background Nevanlinna was born Rolf Herman Neovius, becoming Nevanlinna in 1906 when his fa ...

potential theory In mathematics and mathematical physics, potential theory is the study of harmonic functions. The term "potential theory" was coined in 19th-century physics when it was realized that two fundamental forces of nature known at the time, namely gra ...

, conformal maps and quasiconformal mapping, as well as

Riemann surface In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed ver ...

s. In 1957 Pfluger's monograph ''Theorie der Riemannschen Flächen'' was published in

Springer Springer or springers may refer to: Publishers * Springer Science+Business Media, aka Springer International Publishing, a worldwide publishing group founded in 1842 in Germany formerly known as Springer-Verlag. ** Springer Nature, a multinationa ...

's series ''Grundlehren der mathematischen Wissenschaften''. With Joseph Hersch, he introduced in 1952 a function (now called the Hersch-Pfluger distortion function) useful in estimating the distortion of quasiconformal mappings.Joseph Hersch und Albert Pfluger, ''Généralisation du lemme de Schwarz et du principe de la mesure harmonique pour les fonctions pseudo-analytiques''. Comptes Rendus de l'Académie des Sciences Paris, Tome 234, pp. 43-45, 1952. Entire functions with certain regularity properties were introduced and extensively studied by Pfluger and

Boris Levin Boris Yakovlevich Levin ( rus, Борис Яковлевич Левин, 22 December 1906 – 24 August 1993) was a Soviet mathematician who made significant contributions to complex analysis, function theory. Biography Boris Yakovlevich Levin ...

; these functions are now referred to as functions of completely regular growth in the sense of Levin and Pfluger. Pfluger served a two-year term as president of the

Swiss Mathematical Society The Swiss Mathematical Society (german: Schweizerische Mathematische Gesellschaft; french: Société Mathématique Suisse), founded in Basel on September 4, 1910, is the national mathematical society of Switzerland and a member society of the Europ ...

in 1950–1951. In 1973 he was elected a foreign member of the

Finnish Academy of Sciences The Finnish Academy of Science and Letters (Finnish ''Suomalainen Tiedeakatemia''; Latin ''Academia Scientiarum Fennica'') is a Finnish learned society. It was founded in 1908 and is thus the second oldest academy in Finland. The oldest is the Fi ...

. His doctoral students include Peter Henrici and

Heinz Rutishauser Heinz Rutishauser (30 January 1918 – 10 November 1970) was a Swiss mathematician and a pioneer of modern numerical mathematics and computer science. Life Rutishauser's father died when he was 13 years old and his mother died three years lat ...

. Pfluger was married since 1938 to Maria Jeger.

Selected publications

*with G. Pólya: "On the power series of an integral function having an exceptional value." In Mathematical Proceedings of the Cambridge Philosophical Society, vol. 31, no. 2, pp. 153–155. Cambridge University Press, 1935. *"On analytic functions bounded at the lattice points." Proceedings of the London Mathematical Society 2, no. 1 (1937): 305–315.
"Die Wertverteilung und das Verhalten von Betrag und Argument einer speziellen Klasse analytischer Funktionen."
Commentarii Mathematici Helvetici 11 (1938): 180–214. *"Zur Defektrelation ganzer Funktionen endlicher Ordnung." Commentarii Mathematici Helvetici 19, no. 1 (1946): 91–104. *"Quasikonforme Abbildungen und logarithmische Kapazität." Ann. Inst. Fourier 2 (1950): 69–80. *"Zur Stabilität des tangential gedrückten Stabes." ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 35, no. 5 (1955): 191. *"Extremallängen und Kapazität." Commentarii Mathematici Helvetici 29, no. 1 (1955): 120–131. *"Über die Äquivalenz der geometrischen und der analytischen Definition quasikonformer Abbildungen." Commentarii Mathematici Helvetici 33, no. 1 (1959): 23–33.

Sources

* Hans Künzi
''Zum Gedenken an Albert Pfluger, 1907-1993''
Elemente der Mathematik, Band 49, Heft 3, S. 89–91, 1994. * Joseph Hersch (ed.)
''Complex analysis: articles dedicated to Albert Pfluger on the occasion of his 80. birthday.''
Birkhäuser 1988

References

{{DEFAULTSORT:Pfluger, Albert Swiss mathematicians ETH Zurich alumni ETH Zurich faculty 1907 births 1993 deaths