Friederich Ignaz Mautner
{{short description|Austrian-American mathematician}}
{{Infobox scientist
| name = Friederich I. Mautner
| image =
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| birth_date = {{birth date |1921|05|14}}
| birth_place = Vienna, First Austrian Republic
| death_date = 1996
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| nationality = Austrian American
| fields = Mathematics
| workplaces = Johns Hopkins University
| alma_mater = Princeton University
| doctoral_advisor = John von Neumann
| doctoral_students = Joseph Shalika
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Friederich Ignaz Mautner (14 May 1921–2002)Biographical information from [http://www.oemg.ac.at/Tagungen/2001/KuehlerAbschied.pdf Kühler Abschied - Wien 1938 und der Exodus der Mathematik, Ausstellung der Österreichischen Mathematischen Gesellschaft in der Universität Wien 2001] was an Austrian-American mathematician, known for his research on the representation theory of groups, functional analysis, and differential geometry. He is known for Mautner's Lemma and Mautner's Phenomenon in the representation theory of Lie groups.{{cite journal|author=Moore, Calvin C.|authorlink=Calvin C. Moore|title=The Mautner phenomenon for general unitary representations|journal=Pacific J. Math.|year=1980|volume=86|issue=1|pages=155–169|url=https://projecteuclid.org/journals/pacific-journal-of-mathematics/volume-86/issue-1/The-Mautner-phenomenon-for-general-unitary-representations/pjm/1102780621.full|doi=10.2140/pjm.1980.86.155|doi-access=free}}
Life and career
Following the Anschluss in 1938, Mautner, a Jew, emigrated from Austria to the UK where he became one of the thousands or refugees who were interred by the British and shipped off to Hay Camp 7 in Australia. While there he was fortunate in that he got to study mathematics under Felix Behrend. When he got back to the UK, he garnered a BSc at Durham University and then went to Ireland in 1944 where he got an assistantship with Paul Ewald at Queens University Belfast (QUB).[https://books.google.com/books?id=WKsDDgAAQBAJ&dq=friederich+Mautner+math+johns+hopkins+1921&pg=PA344 An Irish Sanctuary] by Gisela Holfter and Horst Dickel, Walter de Gruyter GmbH, Berlin, p. 344, ISBN 978-3-11-035144-6 He then became a scholar at the Dublin Institute for Advanced Studies in 1944–1946.[http://www.dias.ie/index.php?option=com_content&view=article&id=405:mautner-f-i&catid=44:theoreticalpastmembers&lang=en Mautner, F.I. 1944–46 Scholar, Dublin Institute for Advanced Studies]
He then moved to the USA, where he was a visiting scholarHe would again be at the IAS in 1954-56 and in 1965-66. at the Institute for Advanced Study (IAS) in Princeton (1946-47).[https://www.ias.edu/people/cos/users/5187 Mautner, Friederich I., Institute for Advanced Study]
He then attended Princeton University and got a Ph.D. in 1948 with the thesis Unitary Representations of Infinite Groups.{{MathGenealogy|id=29117|title=Friederich I. Mautner}}
He was a Guggenheim Fellow at Johns Hopkins University in the academic year 1954-55.[https://www.gf.org/fellows/friederich-i-mautner/ Friederich I. Mautner; Fellow: Awarded 1954; Field of Study: Mathematics] John Simon Guggenheim Memorial Foundation
Working in the fields of ergodic theory of geodesic flows, he published a paper in 1957 that established the lemma and the phenomenon that bear his name.Mautner Geodesic flows on symmetric Riemannian spaces, Annals of Mathematics, vol. 65, 1957, pp. 416-430
He published a ground-breaking paper in 1958 that established him as a pioneer in the representation theory of reducible p-adic groups.Mautner Spherical functions over p-adic fields. I, Amer. J. Math. 80 (1958), 441–457; Part 2 appeared 6 years later in Amer. J. Math., vol. 86, 1964, S. 171-200
The Mautner Group, a special five-dimensional Lie group, is named after him.[http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.mmj/1029003351&page=record Baggett, Merrill Representations of the Mautner group and cocycles of an irrational rotation Michigan Math. J., vol. 33, 1986, 221-229]
Frederich had one daughter, Jean Mautner.
Selected works
- {{cite journal|title=The Completeness of the Irreducible Unitary Representations of a Locally Compact Group|journal=Proc Natl Acad Sci U S A|date=February 1948|volume=34|issue=2|pages=52–54|pmc=1062914|doi=10.1073/pnas.34.2.52|pmid=16588786|last1=Mautner|first1=F. I.|doi-access=free}}
- {{cite journal|title=Unitary representations of locally compact groups I|journal=Annals of Mathematics|series=Second Series|year=1950|volume=51|issue=1|pages=1–24|doi=10.2307/1969494|jstor=1969494|last1=Mautner|first1=F. I.}}
- {{cite journal|title=Unitary representations of locally compact groups II|journal=Annals of Mathematics|series=Second Series|volume=52|issue=3|year=1950|pages=528–556|doi=10.2307/1969431|jstor=1969431|last1=Mautner|first1=F. I.}}
- {{cite journal|title=Infinite-dimensional irreducible representations of certain groups|journal=Proc. Amer. Math. Soc.|year=1950|volume=1|issue=5|pages=582–584|mr=0039728|doi=10.1090/s0002-9939-1950-0039728-2|last1=Mautner|first1=F. I.|doi-access=free}}
- {{cite journal|title=The regular representation of a restricted product of finite groups|journal=Trans. Amer. Math. Soc.|year=1951|volume=70|issue=3|pages=531–548|mr=0041855|doi=10.1090/s0002-9947-1951-0041855-6|last1=Mautner|first1=F. I.|doi-access=free}}
- {{cite journal|title=On the decomposition of unitary representations of Lie groups|journal=Proc. Amer. Math. Soc.|year=1951|volume=2|issue=3|pages=490–496|mr=0041856|doi=10.1090/s0002-9939-1951-0041856-3|last1=Mautner|first1=F. I.|doi-access=free}}
- {{cite journal|title=A Generalization of the Frobenius Reciprocity Theorem|journal=Proc Natl Acad Sci U S A|date=July 1951|volume=37|issue=7|pages=431–435|pmc=1063394|pmid=16578378|doi=10.1073/pnas.37.7.431|last1=Mautner|first1=F. I.|doi-access=free}}
- {{cite journal|title=Fourier Analysis and Symmetric Spaces|journal=Proc Natl Acad Sci U S A|date=August 1951|volume=37|issue=8|pages=529–533|pmc=1063414|pmid=16578390|doi=10.1073/pnas.37.8.529|last1=Mautner|first1=F. I.|doi-access=free}}
- {{cite journal|title=On Eigenfunction Expansions|journal=Proc Natl Acad Sci U S A|date=January 1953|volume=39|issue=1|pages=49–53|pmc=1063724|pmid=16589235|doi=10.1073/pnas.39.1.49 |last1=Mautner|first1=F. I.|doi-access=free}}
- {{cite journal|title=Geodesic Flows and Unitary Representations|journal=Proc Natl Acad Sci U S A|date=January 1954|volume=40|issue=1|pages=33–36|pmc=527933|pmid=16589421|doi=10.1073/pnas.40.1.33|last1=Mautner|first1=F. I.|doi-access=free}}
- with L. Ehrenpreis: {{cite journal|title=Uniformly bounded representations of groups|journal=Proc Natl Acad Sci U S A|date=15 April 1955|volume=41|issue=4|pages=231–233|pmc=528064|pmid=16589653|doi=10.1073/pnas.41.4.231|last1=Ehrenpreis|first1=L.|last2=Mautner|first2=F. I.|doi-access=free}}
- {{cite journal|title=Note on the Fourier inversion formula on groups|journal=Trans. Amer. Math. Soc.|year=1955|volume=78|issue=2|pages=371–384|mr=0067230|doi=10.1090/s0002-9947-1955-0067230-x|last1=Mautner|first1=F. I.|doi-access=free}}
- with L. Ehrenpreis: {{cite journal|title=Some properties of the Fourier transform on semi-simple Lie groups. II|journal=Trans. Amer. Math. Soc.|year=1957|volume=84|pages=1–55|mr=0083683|doi=10.1090/s0002-9947-1957-0083683-7|last1=Ehrenpreis|first1=L.|last2=Mautner|first2=F. I.|doi-access=free}}
- with L. Ehrenpreis: {{cite journal|title=Some properties of the Fourier transform on semi-simple Lie groups. III|journal=Trans. Amer. Math. Soc.|year=1957|volume=90|issue=3|pages=431–484|mr=0102755|doi=10.1090/s0002-9947-1959-0102755-3|last1=Ehrenpreis|first1=L.|last2=Mautner|first2=F. I.|doi-access=free}}
References
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Category:20th-century American mathematicians
Category:Austrian emigrants to the United States