Friederich Ignaz Mautner
Friederich Ignaz Mautner (1921–1996)[1] was an Austrian-American mathematician, known for his research on the representation theory of groups, functional analysis, and differential geometry.
Friederich I. Mautner | |
|---|---|
| Born | 1921 |
| Died | 1996 |
| Nationality | Austrian American |
| Alma mater | Princeton University |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Johns Hopkins University |
| Doctoral advisor | John von Neumann |
| Doctoral students | Joseph Shalika |
Mautner, a Jew, emigrated from Austria after the Anschluss via the U.K. and Ireland to the U.S.A. He received in 1948 a Ph.D. from Princeton University with thesis Unitary Representations of Infinite Groups.[2] He taught at Johns Hopkins University and then at the University of Paris and in Italy.
Mautner was an assistant at the Queen's University Belfast and a scholar at the Dublin Institute for Advanced Studies in 1944–1946.[3] He was a visiting scholar at the Institute for Advanced Study in 1946/47, 1954/56, and 1965/66.[4] He was a Guggenheim Fellow in the academic year 1954/55.
He is known for Mautner's Lemma and Mautner's Phenomenon[5] in the representation theory of Lie groups. Mautner's work on the lemma and the phenomenon was done in connection with the ergodic theory of geodesic flows.[6] With a ground-breaking paper in 1958, Mautner became an important pioneer in the representation theory of reducible p-adic groups.[7] The Mautner Group, a special five-dimensional Lie group, is named after him.[8]
His doctoral students include Joseph Shalika.
Selected works
- 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 Frobenious 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.
References
- Biographical information from Kühler Abschied - Wien 1938 und der Exodus der Mathematik, Ausstellung der Österreichischen Mathematischen Gesellschaft in der Universität Wien 2001
- Friederich I. Mautner at the Mathematics Genealogy Project
- Mautner, F.I. 1944–46 Scholar, Dublin Institute for Advanced Studies
- Mautner, Friederich I., Institute for Advanced Study
- 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.
- 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
