Austrian-American mathematician
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]
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 .[ 7]
He was a Guggenheim Fellow at Johns Hopkins University in the academic year 1954-55.[ 8]
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.[ 9]
He published a ground-breaking paper in 1958 that established him as a pioneer in the representation theory of reducible p-adic groups .[ 10]
The Mautner Group, a special five-dimensional Lie group , is named after him.[ 11]
Frederich had one daughter, Jean Mautner.
Mautner, F. I. (February 1948). "The Completeness of the Irreducible Unitary Representations of a Locally Compact Group" . Proc Natl Acad Sci U S A . 34 (2): 52–54. doi :10.1073/pnas.34.2.52 . PMC 1062914 . PMID 16588786 .
Mautner, F. I. (1950). "Unitary representations of locally compact groups I". Annals of Mathematics . Second Series. 51 (1): 1–24. doi :10.2307/1969494 . JSTOR 1969494 .
Mautner, F. I. (1950). "Unitary representations of locally compact groups II". Annals of Mathematics . Second Series. 52 (3): 528–556. doi :10.2307/1969431 . JSTOR 1969431 .
Mautner, F. I. (1950). "Infinite-dimensional irreducible representations of certain groups" . Proc. Amer. Math. Soc . 1 (5): 582–584. doi :10.1090/s0002-9939-1950-0039728-2 . MR 0039728 .
Mautner, F. I. (1951). "The regular representation of a restricted product of finite groups" . Trans. Amer. Math. Soc . 70 (3): 531–548. doi :10.1090/s0002-9947-1951-0041855-6 . MR 0041855 .
Mautner, F. I. (1951). "On the decomposition of unitary representations of Lie groups" . Proc. Amer. Math. Soc . 2 (3): 490–496. doi :10.1090/s0002-9939-1951-0041856-3 . MR 0041856 .
Mautner, F. I. (July 1951). "A Generalization of the Frobenius Reciprocity Theorem" . Proc Natl Acad Sci U S A . 37 (7): 431–435. doi :10.1073/pnas.37.7.431 . PMC 1063394 . PMID 16578378 .
Mautner, F. I. (August 1951). "Fourier Analysis and Symmetric Spaces" . Proc Natl Acad Sci U S A . 37 (8): 529–533. doi :10.1073/pnas.37.8.529 . PMC 1063414 . PMID 16578390 .
Mautner, F. I. (January 1953). "On Eigenfunction Expansions" . Proc Natl Acad Sci U S A . 39 (1): 49–53. doi :10.1073/pnas.39.1.49 . PMC 1063724 . PMID 16589235 .
Mautner, F. I. (January 1954). "Geodesic Flows and Unitary Representations" . Proc Natl Acad Sci U S A . 40 (1): 33–36. doi :10.1073/pnas.40.1.33 . PMC 527933 . PMID 16589421 .
with L. Ehrenpreis : Ehrenpreis, L.; Mautner, F. I. (15 April 1955). "Uniformly bounded representations of groups" . Proc Natl Acad Sci U S A . 41 (4): 231–233. doi :10.1073/pnas.41.4.231 . PMC 528064 . PMID 16589653 .
Mautner, F. I. (1955). "Note on the Fourier inversion formula on groups" . Trans. Amer. Math. Soc . 78 (2): 371–384. doi :10.1090/s0002-9947-1955-0067230-x . MR 0067230 .
with L. Ehrenpreis: Ehrenpreis, L.; Mautner, F. I. (1957). "Some properties of the Fourier transform on semi-simple Lie groups. II" . Trans. Amer. Math. Soc . 84 : 1–55. doi :10.1090/s0002-9947-1957-0083683-7 . MR 0083683 .
with L. Ehrenpreis: Ehrenpreis, L.; Mautner, F. I. (1957). "Some properties of the Fourier transform on semi-simple Lie groups. III" . Trans. Amer. Math. Soc . 90 (3): 431–484. doi :10.1090/s0002-9947-1959-0102755-3 . MR 0102755 .
^ Biographical information from Kühler Abschied - Wien 1938 und der Exodus der Mathematik , Ausstellung der Österreichischen Mathematischen Gesellschaft in der Universität Wien 2001
^ Moore, Calvin C. (1980). "The Mautner phenomenon for general unitary representations" . Pacific J. Math . 86 (1): 155–169. doi :10.2140/pjm.1980.86.155 .
^ An Irish Sanctuary by Gisela Holfter and Horst Dickel, Walter de Gruyter GmbH, Berlin, p. 344, ISBN 978-3-11-035144-6
^ Mautner, F.I. 1944–46 Scholar, Dublin Institute for Advanced Studies
^ He would again be at the IAS in 1954-56 and in 1965-66.
^ Mautner, Friederich I., Institute for Advanced Study
^ Friederich I. Mautner at the Mathematics Genealogy Project
^ Friederich I. Mautner; Fellow: Awarded 1954; Field of Study: Mathematics John Simon Guggenheim Memorial Foundation
^ Mautner Geodesic flows on symmetric Riemannian spaces , Annals of Mathematics, vol. 65, 1957, pp. 416-430
^ 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
^ Baggett, Merrill Representations of the Mautner group and cocycles of an irrational rotation Michigan Math. J., vol. 33, 1986, 221-229