Carl S. Herz

Carl Samuel Herz (10 April 1930, Rockville Centre, Long Island, New York – 1 May 1995) was an American-Canadian mathematician, specializing in harmonic analysis. His name is attached to the Herz–Schur multiplier.

Education and career

Herz received his bachelor's degree from Cornell University in 1950 and then became a mathematics graduate student at Princeton University. There he received a Ph.D. under the supervision of Salomon Bochner in 1953 with the dissertation "Bessel Functions of Matrix Argument".^[1] According to Tom H. Koornwinder, Herz's dissertation (published in the Annals of Mathematics in May 1955) "was a pioneering paper in the field of special functions in several variables associated with Lie groups and with root systems."^[2] Herz returned to Cornell, where he became in 1953 an instructor, in 1955 an assistant professor, in 1958 an associate professor, and in 1963 a full professor and remained at Cornell until 1969. He worked for the academic year 1969–1970 at Brandeis University and then became in 1970 a professor at McGill University, where he remained until his death in 1995. For the academic year 1962–1963 Herz was a Sloan Fellow at Université de Paris-Sud at Orsay; in subsequent years he was a frequent academic visitor at Orsay for a month or two each year. In the academic years 1957-1958 and 1976–1977 he was a visiting scholar at the Institute for Advanced Study. Herz did mathematical research on spectral synthesis, positive definite functions, Fourier transforms on convex sets, potential theory, H_p, and BMO. According to Nicholas Varopoulos, Herz made contributions "to the theory of symmetric spaces, Lie groups and the heat kernel on these; among other things he succeeded in classifying all faithful representations of Lie groups by contact transformations of a compact manifold."^[3]

In 1978 he was elected of a Fellow of the Royal Society of Canada. In 1986 he was awarded the Jeffery–Williams Prize by the Canadian Mathematical Society. The Institut des sciences mathématiques (a consortium of eight Quebec universities) established a prize in honour of Carl Herz.^[4] He was the president of the Canadian Mathematical Society in 1987–1989.^[5]

Selected publications

• "On the mean inversion of Fourier and Hankel transforms" (PDF). Proc Natl Acad Sci U S A 40 (10): 996–999. 1954. doi:10.1073/pnas.40.10.996.
• "Bessel functions of matrix argument". Annals of Math. 61 (3): 474–523. May 1955. doi:10.2307/1969810.
• "Spectral synthesis for the Cantor set" (PDF). Proc Natl Acad Sci U S A 42 (1): 42–43. 1956. doi:10.1073/pnas.42.1.42.
• "A note on summability methods and spectral theory". Trans. Amer. Math. Soc. 86: 506–510. 1957. doi:10.1090/s0002-9947-1957-0093685-2. MR 0093685.
• "A note on the span of translations in L^p". Proc. Amer. Math. Soc. 8: 724–727. 1957. doi:10.1090/s0002-9939-1957-0088604-4. MR 0088604.
• "The spectral theory of bounded functions". Trans. Amer. Math. Soc. 94: 181–232. 1960. doi:10.1090/s0002-9947-1960-0131779-3. MR 0131779.
• "A maximal theorem". Proc. Amer. Math. Soc. 12: 229–233. 1961. doi:10.1090/s0002-9939-1961-0151861-0. MR 0151861.
• "A class of negative-definite functions". Proc. Amer. Math. Soc. 14: 670–676. 1963. doi:10.1090/s0002-9939-1963-0158251-7. MR 0158251.
• "The theory of p-spaces with an application to convolution operators". Trans. Amer. Math. Soc. 154: 69–82. 1971. doi:10.1090/s0002-9947-1971-0272952-0. MR 0272952.
• "Bounded mean oscillation and regulated martingales". Trans. Amer. Math. Soc. 193: 199–215. 1974. doi:10.1090/s0002-9947-1974-0353447-5. MR 0353447.
• "The derivative of the exponential map". Proc. Amer. Math. Soc. 112 (3): 909–911. 1991. doi:10.1090/s0002-9939-1991-1086328-8. MR 1086328.

References

1. Carl Herz at the Mathematics Genealogy Project
2. Koornwinder, T. H. (12 September 1996). "Death of Carl Herz". OP–SF WEB.
3. "Carl Herz 1930--1995" (PDF). Notices of the AMS 43 (7): 768–771. July 1996.
4. The Carl Herz Prize, Institut des sciences mathématiques.
5. Carl Herz, ISM