Friederich Ignaz Mautner (1921–2001) 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. 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. He was a visiting scholar at the Institute for Advanced Study in 1946/47, 1954/56, and 1965/66. He was a Guggenheim Fellow in the academic year 1954/55.
He is known for Mautner's Lemma and Mautner's Phenomenon 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. With a ground-breaking paper in 1958, Mautner became an important pioneer in the representation theory of reducible p-adic groups. The Mautner Group, a special five-dimensional Lie group, is named after him.
His doctoral students include Joseph Shalika.
"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 . PMID 16588786. doi:10.1073/pnas.34.2.52.
"Unitary representations of locally compact groups I". Annals of Mathematics. Second Series. 51 (1): 1–24. 1950. JSTOR 1969494. doi:10.2307/1969494.
"Unitary representations of locally compact groups II". Annals of Mathematics. Second Series. 52 (3): 528–556. 1950. JSTOR 1969431. doi:10.2307/1969431.
"Infinite-dimensional irreducible representations of certain groups". Proc. Amer. Math. Soc. 1: 582–584. 1950. MR 0039728. doi:10.1090/s0002-9939-1950-0039728-2.
"The regular representation of a restricted product of finite groups". Trans. Amer. Math. Soc. 70: 531–548. 1951. MR 0041855. doi:10.1090/s0002-9947-1951-0041855-6.
"On the decomposition of unitary representations of Lie groups". Proc. Amer. Math. Soc. 2: 490–496. 1951. MR 0041856. doi:10.1090/s0002-9939-1951-0041856-3.
"A Generalization of the Frobenious Reciprocity Theorem". Proc Natl Acad Sci U S A. 37 (7): 431–435. July 1951. PMC 1063394 . PMID 16578378. doi:10.1073/pnas.37.7.431.
"Fourier Analysis and Symmetric Spaces". Proc Natl Acad Sci U S A. 37 (8): 529–533. August 1951. PMC 1063414 . PMID 16578390. doi:10.1073/pnas.37.8.529.
"On Eigenfunction Expansions". Proc Natl Acad Sci U S A. 39 (1): 49–53. January 1953. PMC 1063724 . PMID 16589235. doi:10.1073/pnas.39.1.49.
"Geodesic Flows and Unitary Representations". Proc Natl Acad Sci U S A. 40 (1): 33–36. January 1954. PMC 527933 . PMID 16589421. doi:10.1073/pnas.40.1.33.
with L. Ehrenpreis: "Uniformly bounded representations of groups". Proc Natl Acad Sci U S A. 41 (4): 231–233. 15 April 1955. PMC 528064 . PMID 16589653. doi:10.1073/pnas.41.4.231.
"Note on the Fourier inversion formula on groups". Trans. Amer. Math. Soc. 78: 371–384. 1955. MR 0067230. doi:10.1090/s0002-9947-1955-0067230-x.
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. doi:10.1090/s0002-9947-1957-0083683-7.
with L. Ehrenpreis: "Some properties of the Fourier transform on semi-simple Lie groups. III". Trans. Amer. Math. Soc. 90: 431–484. 1957. MR 0102755. doi:10.1090/s0002-9947-1959-0102755-3.
