François Trèves Explained

Birth Name:	Jean François Trèves
Birth Date:	23 April 1930
Birth Place:	Brussels
Citizenship:	Italian until 1972, also USA since 1972
Fields:	Mathematics
Workplaces:	University of California, Berkeley Yeshiva University; Purdue University; Rutgers University
Education:	Paris-Sorbonne University
Academic Advisors:	Laurent Schwartz
Known For:	Partial differential equations
Awards:	Chauvenet Prize, Guggenheim Fellow, Leroy P. Steele Prize; Bergman Prize; foreign member of the Brazilian Academy of Sciences; Doctorate Honoris Causa, University of Pisa, Italy; fellow of the American Mathematical Society

J. (Jean) François Treves (born April 23, 1930, in Brussels) is an American mathematician, specializing in partial differential equations.

Trèves earned his Ph.D. in 1958 from Paris-Sorbonne University under the supervision of Laurent Schwartz. He then went to the United States where from 1958 to 1960 he was assistant professor at the University of California, Berkeley. From 1961 to 1964 he was an associate professor at Yeshiva University, and from 1964 to 1970 professor at Purdue University. In 1970 he became a professor at Rutgers University, and then, in 1984, Robert-Adrian professor of mathematics. He became professor emeritus in 2005.

In 1972 he received the Chauvenet Prize for "On local solvability of linear partial differential equations" in the Bulletin of the AMS (Volume 76, 1970, pp. 552–571). It was about the problem he worked in 1962 with Louis Nirenberg with whom he found necessary and sufficient conditions for the solvability of equations with analytic coefficients, 1969 (Comptes Rendus de l'Académie des Sciences Paris Bd.269). The question was first presented to him in 1955 by Schwartz as a thesis problem.

In 1977 he was Guggenheim Fellow. In 1991 he received the Leroy P. Steele Prize for his book on pseudo-differential operators and Fourier integral operators. In 2003 he became a foreign member of the Brazilian Academy of Sciences. In 1970 he was an invited speaker at the International Congress of Mathematicians in Nice (Hamiltonian fields, bicharacteristic strips in relation with existence and regularity of solutions of linear partial differential equations).^[1] He is a fellow of the American Mathematical Society.^[2]

Writings

Articles

• "On the theory of linear partial differential operators with analytic coefficients." Transactions of the American Mathematical Society 137 (1969): 1–20.
• "An abstract nonlinear Cauchy-Kovalevska theorem." Transactions of the American Mathematical Society 150, no. 1 (1970): 77–92.
• "Differential polynomials and decay at infinity." Bulletin of the American Mathematical Society 66, no. 3 (1960): 184–186.
• "Discrete phenomena in uniqueness in the Cauchy problem." Proceedings of the American Mathematical Society 46, no. 2 (1974): 229–233.
• with Howard Jacobowitz: "Nowhere solvable homogeneous partial differential equations." Bulletin of the American Mathematical Society 8, no. 3 (1983): 467–469.
• with Nicholas Hanges: "On the analyticity of solutions of first-order nonlinear PDE." Transactions of the American Mathematical Society 331, no. 2 (1992): 627–638.

Books

• Book: Treves, François . Locally Convex Spaces and Linear Partial Differential Equations . 1967 . Springer Berlin Heidelberg . 978-3-642-87373-7 . Berlin, Heidelberg . 10.1007/978-3-642-87371-3 . 2022-09-13.
• Book: Treves, François . Linear Partial Differential Equations with Constant Coefficients . 1968 . Gordon and Breach . New York, N. Y. .
• Book: Treves, François . Analytic Partial Differential Equations . 2022 . Springer International Publishing . 978-3-030-94054-6 . Grundlehren der mathematischen Wissenschaften . 359 . Cham . 10.1007/978-3-030-94055-3 . 2022-09-13.
• Book: Treves, François . Introduction to Pseudodifferential and Fourier Integral Operators Volume 1 . 1980 . Springer US . 978-1-4684-8782-4 . Boston, MA . 10.1007/978-1-4684-8780-0 . 2022-09-13.
• Book: Treves, Francois . Basic linear partial differential equations . 2006 . Dover Publications . 978-0-486-45346-0 . Dover books on mathematics . Mineola, N.Y.
• Book: Treves, Francois . Topological vector spaces, distributions and kernels . 2006 . Dover Publications . 978-0-486-45352-1 . Dover books on mathematics . Mineola, N.Y.
• Book: Cordaro . Paulo D. . Hyperfunctions on hypo-analytic manifolds . Treves . Francois . 1994 . Princeton University Press . 978-0-691-02993-1 . Annals of mathematics studies . Princeton, N.J. ^[3]
• Book: Treves, François . Hypo-Analytic Structures (PMS-40), Volume 40: Local Theory (PMS-40) . 2014 . Princeton University Press . 978-0-691-63541-5 . Course Book . Princeton, NJ. ^[4]
• Book: Treves, Francois . Homotopy formulas in the tangential Cauchy-Riemann complex . 1990 . American Mathematical Society . 978-1-4704-0857-2 . Providence, R.I., USA.

External links

• Trèves: On local solvability of linear partial differential equations. BAMS 1970
• Rutgers University: emeritus status in 2005

Notes and References

1. Trèves, F. "Hamiltonian fields, bicharactertistic strips in relation with existence and regularity of solutions of linear partial differential equations." In Actes, Congrès Intern. Math, vol. 2, pp. 803–811. 1970.
2. https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society
3. Schapira, Pierre. Pierre Schapira (mathematician). Review: Hyperfunctions on hypo-analytic manifolds by Paulo D. Cordaro and François Trèves. Bull. Amer. Math. Soc. (N.S.). 1996. 33. 1. 115–118. 10.1090/s0273-0979-96-00628-3. free.
4. Webster, Sidney M.. Sidney Martin Webster. Review: Hypo-analytic structures, local theory by François Trèves. Bull. Amer. Math. Soc. (N.S.). 1994. 30. 2. 290–292. 10.1090/s0273-0979-1994-00468-9. free.