Friederich Ignaz Mautner

Friederich Ignaz Mautner (1921, Vienna – 1996)^[1] was an American mathematician, known for his research on the representation theory of groups, functional analysis, and differential geometry.

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

• "The Completeness of the Irreducible Unitary Representations of a Locally Compact Group". Proc Natl Acad Sci U S A 34 (2): 52–54. February 1948. PMC 1062914. 
• "Unitary representations of locally compact groups I". Annals of Mathematics. Second Series 51 (1): 1–24. 1950. 
• "Unitary representations of locally compact groups II". Annals of Mathematics. Second Series 52 (3): 528–556. 1950. 
• "Infinite-dimensional irreducible representations of certain groups". Proc. Amer. Math. Soc. 1: 582–584. 1950. MR 0039728. 
• "The regular representation of a restricted product of finite groups". Trans. Amer. Math. Soc. 70: 531–548. 1951. MR 0041855. 
• "On the decomposition of unitary representations of Lie groups". Proc. Amer. Math. Soc. 2: 490–496. 1951. MR 0041856. 
• "A Generalization of the Frobenious Reciprocity Theorem". Proc Natl Acad Sci U S A 37 (7): 431–435. July 1951. PMC 1063394. 
• "Fourier Analysis and Symmetric Spaces". Proc Natl Acad Sci U S A 37 (8): 529–533. August 1951. PMC 1063414. 
• "On Eigenfunction Expansions". Proc Natl Acad Sci U S A 39 (1): 49–53. January 1953. PMC 1063724. 
• "Geodesic Flows and Unitary Representations". Proc Natl Acad Sci U S A 40 (1): 33–36. January 1954. PMC 527933. 
• with L. Ehrenpreis: "Uniformly bounded representations of groups". Proc Natl Acad Sci U S A 41 (4): 231–233. 15 April 1955. PMC 528064. 
• "Note on the Fourier inversion formula on groups". Trans. Amer. Math. Soc. 78: 371–384. 1955. MR 0067230. 
• with L. Ehrenpreis: "Some properties of the Fourier transform on semi-simple Lie groups. II". Trans. Amer. Math. Soc. 84: 1–55. 1957. MR 0083683. 
• with L. Ehrenpreis: "Some properties of the Fourier transform on semi-simple Lie groups. III". Trans. Amer. Math. Soc. 84: 431–484. 1957. MR 0102755. 

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. ↑ Friederich I. Mautner at the Mathematics Genealogy Project
3. ↑ Mautner, F.I. 1944–46 Scholar, Dublin Institure for Advanced Studies
4. ↑ Mautner, Friederich I., Institute for Advanced Study
5. ↑ Moore, Calvin C. (1980). "The Mautner phenomenon for general unitary representations". Pacific J. Math. 86 (1): 155–169. 
6. ↑ Mautner Geodesic flows on symmetric Riemannian spaces, Annals of Mathematics, vol. 65, 1957, pp. 416-430
7. ↑ 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
8. ↑ Baggett, Merrill Representations of the Mautner group and cocycles of an irrational rotation Michigan Math. J., vol. 33, 1986, 221-229