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**Paul Robert Chernoff** (21 June 1942, Philadelphia – 17 January 2017)^{[1]} was an American mathematician, specializing in functional analysis and the mathematical foundations of quantum mechanics.^{[2]} He is known for Chernoff's Theorem, a mathematical result in the Feynman path integral formulation of quantum mechanics.^{[3]}

Chernoff graduated from Central High School in Philadelphia. He matriculated at Harvard University, where he received bachelor's degree, *summa cum laude*, in 1963, master's degree in 1965, and Ph.D. in 1968 under George Mackey with thesis *Semigroup Product Formulas and Addition of Unbounded Operators*.^{[4]}

At the University of California, Berkeley, he became in 1969 a lecturer, in 1971 an assistant professor, and in 1980 a full professor. U. C. Berkeley awarded him multiple Distinguished Teaching Awards and the Lili Fabilli and Eric Hoffer Essay Prize.^{[2]} In 1986 he was a visiting professor at the University of Pennsylvania.

Chernoff was elected in 1984 a Fellow of the American Association for the Advancement of Science^{[5]} and in 2012 a Fellow of the American Mathematical Society.

He gave in 1981 a simplified proof of the Groenewold-Van Hove theorem,^{[6]}^{[7]}^{[8]} which is a no-go theorem that relates classical mechanics to quantum mechanics.^{[2]}

- Note on product formulas for operator semigroups, J. Funct. Analysis, vol. 2, 1968, pp. 238–242 doi:10.1016/0022-1236(68)90020-7
- with Richard Anthony Rasala and William C. Waterhouse: The Stone-Weierstrass theorem for valuable fields Pacific Journal of Mathematics vol. 27, no. 2, 1968, pp. 233–240
- Some remarks on quasi-analytic vectors, Trans. Amer. Math. Soc. vol. 167, 1972, pp. 105–113 doi:10.1090/S0002-9947-1972-0295125-5
- Representations, automorphisms, and derivations of some operator algebras, J. Funct. Analysis, vol. 12, 1973, pp. 275–289 doi:10.1016/0022-1236(73)90080-3
- Essential self-adjointness of powers of generators of hyperbolic equations, J. Funct. Analysis, vol. 12, 1973, pp. 401–414 doi:10.1016/0022-1236(73)90003-7
- Product formulas, nonlinear semigroups, and addition of unbounded operators, American Mathematical Society 1974.
- with Jerrold Marsden: Properties of infinite dimensional Hamiltonian systems, Springer 1974
- Understanding mathematical proofs: Conceptual barriers. Science vol. 193, no. 4250, 1976, p. 276
- The quantum
*n*-body problem and a theorem of Littlewood, Pacific J. Math., vol. 70, 1977, pp. 117–123 - Irreducible representations of infinite-dimensional transformation groups and Lie algebras, I. J. Funct. Anal., vol. 130, 1995, pp. 255–282 doi:10.1006/jfan.1995.1069
- with Rhonda Hughes: "A new class of point interactions in one dimension." Journal of functional analysis, vol. 111, no. 1, 1993, pp. 97–117 doi:10.1006/jfan.1993.1006
- with R. Hughes: Some examples related to Kato's conjecture. J. Austral. Math. Soc. Ser. A, vol. 60, 1996, pp. 274–286. doi:10.1017/S1446788700037666
- Quantization and irreducible representations of infinite-dimensional transformation groups and Lie algebras. In: Proceedings of the Symposium on Mathematical Physics and Quantum Field Theory (Berkeley, CA, 1999), Eletron. J. Differ. Equ. Conf., vol. 4, 2000, pp. 17–22
- A pseudo zeta function and the distribution of primes, Proc. Natl. Acad. Sci. USA, vol. 97, 2000, pp. 7697–7699 PMC 16606 (There is a typographical error: "One can show that C(s) may be analytically continued at least into the half-plane Re s > 0 except for an isolated singularity (presumably a simple pole) at s = 0." This should be "at s = 1" according to the mathematical argument given.)

**^**biographical information from*American Men and Women of Science*, Thomson Gale 2004- ^
^{a}^{b}^{c}"Obituary. Paul Chernoff".*San Francisco Chronicle*. 2 April 2017. **^**Butko, Yana A. (2015). "Chernoff approximation of subordinate semigroups and applications".*Stochastics and Dynamics*.**18**(3): 1850021. arXiv:1512.05258. doi:10.1142/S0219493718500211. S2CID 119146783.**^**Paul Robert Chernoff at the Mathematics Genealogy Project**^**"American Association for the Advancement of Science Elects University Members".*University of California Bulletin, week of August 6–10, 1984*. Vol. 33, no. 3. 1984. p. 12.**^**Chernoff, Mathematical obstructions to quantization, Hadronic J., vol. 4, 1981, pp. 879–898**^**Sternberg, Shlomo; Guillemin, Victor (1990).*Symplectic Techniques in Physics*. Cambridge University Press. pp. 101–102. ISBN 9780521389907.**^**Berndt, Rolf (1998).*Einführung in die Symplektische Geometrie*. Vieweg. pp. 119–120. ISBN 9783322802156.