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In 1903, in his final year in school, Alfréd Haar won
first prize in the Eötvös
contest in mathematics. Haar travelled to Germany in 1904 to study at Göttingen
and there he studied under Hilbert's
supervision, obtaining his doctorate in 1909 with a dissertation entitled Zur
Theorie der orthogonalen Funktionensysteme.
Haar then taught at
Göttingen until 1912 when he returned to Hungary and held chairs at the
university in Kolozsvár (which is now Cluj in Romania), Budapest University and
Szeged University. In fact after Word War I Kolozsvár was no longer in Hungary,
so the University there had to move within Hungarian borders and it moved to
Szeged, where there had previously been no university. Haar, together with Riesz,
rapidly made a major mathematical centre from the new university.
Haar worked in analysis. His doctoral thesis studied orthogonal systems of functions. Later he went on to study partial differential equations. He also wrote on Chebyshev approximations and linear inequalities. Between 1917 and 1919 he worked on the variational calculus.
Haar is best remembered for his work on analysis on groups. In 1932 he introduced a measure on groups, now called the Haar measure, which allows an analogue of Lebesgue integrals to be defined on locally compact topological groups. It was used by von Neumann, by Pontryagin in 1934 and Weil in 1940 to set up an abstract theory of commutative harmonic analysis.
Texto original por: J J O'Connor and E F Robertson
Click on this link to see a list of the Glossary entries for this page
| List of References (5 books/articles)
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| A Poster of Alfréd Haar | Mathematicians born in the same country
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| Other references in MacTutor | Chronology: 1930 to 1940 |
| JOC/EFR December 1996 | School of
Mathematics and Statistics University of St Andrews, Scotland | 
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| The URL of this page
is: http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Haar.htm | ||