Friederich Ignaz Mautner Explained

Friederich I. Mautner
Birth Date:	14 May 1921
Birth Place:	Vienna, First Austrian Republic
Death Date:	1996
Nationality:	Austrian American
Fields:	Mathematics
Workplaces:	Johns Hopkins University
Alma Mater:	Princeton University
Doctoral Advisors:	)-->
Doctoral Students:	Joseph Shalika

Friederich Ignaz Mautner (14 May 1921–2002)^[1] 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.^[2]

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).^[3] He then became a scholar at the Dublin Institute for Advanced Studies in 1944–1946.^[4]

He then moved to the USA, where he was a visiting scholar^[5] at the Institute for Advanced Study (IAS) in Princeton (1946-47).^[6]

He then attended Princeton University and got a Ph.D. in 1948 with the thesis Unitary Representations of Infinite Groups.

He was a Guggenheim Fellow at Johns Hopkins University in the academic year 1954-55.^[7]

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.^[8]

He published a ground-breaking paper in 1958 that established him as a pioneer in the representation theory of reducible p-adic groups.^[9]

The Mautner Group, a special five-dimensional Lie group, is named after him.^[10]

Frederich had one daughter, Jean Mautner.

Selected works

• The Completeness of the Irreducible Unitary Representations of a Locally Compact Group. Proc Natl Acad Sci U S A. February 1948. 34. 2. 52–54. 1062914. 10.1073/pnas.34.2.52. 16588786. Mautner. F. I.. free.
• Unitary representations of locally compact groups I. Annals of Mathematics. Second Series. 1950. 51. 1. 1–24. 10.2307/1969494. 1969494. Mautner. F. I..
• Unitary representations of locally compact groups II. Annals of Mathematics. Second Series. 52. 3. 1950. 528–556. 10.2307/1969431. 1969431. Mautner. F. I..
• Infinite-dimensional irreducible representations of certain groups. Proc. Amer. Math. Soc.. 1950. 1. 5. 582–584. 0039728. 10.1090/s0002-9939-1950-0039728-2. Mautner. F. I.. free.
• The regular representation of a restricted product of finite groups. Trans. Amer. Math. Soc.. 1951. 70. 3. 531–548. 0041855. 10.1090/s0002-9947-1951-0041855-6. Mautner. F. I.. free.
• On the decomposition of unitary representations of Lie groups. Proc. Amer. Math. Soc.. 1951. 2. 3. 490–496. 0041856. 10.1090/s0002-9939-1951-0041856-3. Mautner. F. I.. free.
• A Generalization of the Frobenius Reciprocity Theorem. Proc Natl Acad Sci U S A. July 1951. 37. 7. 431–435. 1063394. 16578378. 10.1073/pnas.37.7.431. Mautner. F. I.. free.
• Fourier Analysis and Symmetric Spaces. Proc Natl Acad Sci U S A. August 1951. 37. 8. 529–533. 1063414. 16578390. 10.1073/pnas.37.8.529. Mautner. F. I.. free.
• On Eigenfunction Expansions. Proc Natl Acad Sci U S A. January 1953. 39. 1. 49–53. 1063724. 16589235. 10.1073/pnas.39.1.49 . Mautner. F. I.. free.
• Geodesic Flows and Unitary Representations. Proc Natl Acad Sci U S A. January 1954. 40. 1. 33–36. 527933. 16589421. 10.1073/pnas.40.1.33. Mautner. F. I.. free.
• with L. Ehrenpreis: Uniformly bounded representations of groups. Proc Natl Acad Sci U S A. 15 April 1955. 41. 4. 231–233. 528064. 16589653. 10.1073/pnas.41.4.231. Ehrenpreis. L.. Mautner. F. I.. free.
• Note on the Fourier inversion formula on groups. Trans. Amer. Math. Soc.. 1955. 78. 2. 371–384. 0067230. 10.1090/s0002-9947-1955-0067230-x. Mautner. F. I.. free.
• with L. Ehrenpreis: Some properties of the Fourier transform on semi-simple Lie groups. II. Trans. Amer. Math. Soc.. 1957. 84. 1–55. 0083683. 10.1090/s0002-9947-1957-0083683-7. Ehrenpreis. L.. Mautner. F. I.. free.
• with L. Ehrenpreis: Some properties of the Fourier transform on semi-simple Lie groups. III. Trans. Amer. Math. Soc.. 1957. 90. 3. 431–484. 0102755. 10.1090/s0002-9947-1959-0102755-3. Ehrenpreis. L.. Mautner. F. I.. free.

Notes and References

1. Biographical information from Kühler Abschied - Wien 1938 und der Exodus der Mathematik, Ausstellung der Österreichischen Mathematischen Gesellschaft in der Universität Wien 2001
2. Moore, Calvin C.. Calvin C. Moore. The Mautner phenomenon for general unitary representations. Pacific J. Math.. 1980. 86. 1. 155–169. 10.2140/pjm.1980.86.155. free.
3. An Irish Sanctuary by Gisela Holfter and Horst Dickel, Walter de Gruyter GmbH, Berlin, p. 344, ISBN 978-3-11-035144-6
4. 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
5. He would again be at the IAS in 1954-56 and in 1965-66.
6. https://www.ias.edu/people/cos/users/5187 Mautner, Friederich I., Institute for Advanced Study
7. https://www.gf.org/fellows/friederich-i-mautner/ Friederich I. Mautner; Fellow: Awarded 1954; Field of Study: Mathematics
8. Mautner Geodesic flows on symmetric Riemannian spaces, Annals of Mathematics, vol. 65, 1957, pp. 416-430
9. 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
10. 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