# Gilbert Hunt

Full name Gilbert A. Hunt, Jr. United States March 4, 1916Washington, D.C.[1] May 30, 2008 (aged 92)Princeton, New Jersey[2] Right-handed (one-handed backhand) QF (1938, 1939)

Gilbert Agnew Hunt, Jr. (March 4, 1916 – May 30, 2008)[1] was an American mathematician and amateur tennis player active in the 1930s and 1940s.

## Tennis career

Hunt reached the quarterfinals of the U.S. National Championships in 1938 and 1939.

## Scientific career

Hunt received his bachelor's degree from George Washington University in 1938 and his Ph.D. from Princeton University in 1948 under Salomon Bochner. Hunt became a mathematics professor at Princeton University specializing in probability theory,[2] Markov processes, and potential theory.[1]

The Hunt process is named after him. He was an Invited Speaker at the ICM in 1962 in Stockholm. His doctoral students include Robert McCallum Blumenthal and Richard M. Dudley.

### Hunt's theorem

Hunt's theorem states that for a large class of positive kernels ${\displaystyle V}$ satisfying "the complete maximum principle" of potential theory, there corresponds a contraction resolvent and associated sub-Markovian semigroup ${\displaystyle P_{t}}$ with

${\displaystyle Vf=\int _{0}^{\infty }P_{t}fdt~.}$ (${\displaystyle V}$ is called the "potential kernel" of the semigroup.)[3]

## Selected publications

• "Random Fourier transforms". Trans. Amer. Math. Soc. 71: 38–69. 1951. doi:10.1090/S0002-9947-1951-0051340-3.
• with Paul Erdős: "Changes of sign of sums of random variables". Pacific Journal of Mathematics. 3 (4): 673–687. 1953.
• "On positive Green's functions". Proc. Natl. Acad. Sci. 40 (9): 816–818. 1954. PMID 16589567.
• "An inequality in probability theory". Proc. Amer. Math. Soc. 6: 506–510. 1955. doi:10.1090/S0002-9939-1955-0075470-4.
• "Markoff processes and potentials". Proc. Natl. Acad. Sci. 42 (7): 414–418. 1956. PMID 16589879.
• "Semi-groups of measures on Lie groups". Trans. Amer. Math. Soc. 81: 264–293. 1956. doi:10.1090/S0002-9947-1956-0079232-9.
• "Some theorems concerning Brownian motion". Trans. Amer. Math. Soc. 81: 294–319. 1956. doi:10.1090/S0002-9947-1956-0079377-3.
• "A theorem of Elie Cartan". Proc. Amer. Math. Soc. 7: 307–308. 1956. doi:10.1090/S0002-9939-1956-0077075-9.

## References

1. ^ a b c
2. ^ a b
3. ^ Mitro, Joanna (1991). "Review of Probabilités et potentiel by Claude Dellacherie and Paul-André Meyer, 1987". Bull. Amer. Math. Soc. (N.S.). 24: 471–477. doi:10.1090/S0273-0979-1991-16069-6. (See p. 475.)