Antonio Sa Barreto

Professor of Mathematics

• 765 49-41967

• MATH 640

sabarre@purdue.edu
Personal Website

Research Interest(s):

Partial Differential Equations, Geometric Analysis, Mathematical Physics, Inverse Problems

Selected Publications

• [1] Antônio Sá Barreto. Radiation fields, scattering, and inverse scattering on asymptotically hyperbolic manifolds. Duke Math. J., 129(3):407-480, 2005.
• [2] Antônio Sá Barreto and Jared Wunsch. The radiation field is a Fourier integral operator. Ann. Inst. Fourier (Grenoble), 55(1):213-227, 2005.
• [3] Antônio Sá Barreto. Radiation fields and inverse scattering on asymptotically Euclidean manifolds. In Partial differential equations and inverse problems, volume 362 of Contemp. Math., pages 371-380. Amer. Math. Soc., Providence, RI, 2004.
• [4] Antônio Sá Barreto. Radiation fields on asymptotically Euclidean manifolds. Comm. Partial Differential Equations, 28(9-10):1661-1673, 2003.
• [5] Antonio Sá Barreto. Remarks on the distribution of resonances in odd dimensional Euclidean scattering. Asymptot. Anal., 27(2):161-170, 2001.
• [6] Mark S. Joshi and Antônio Sá Barreto. The wave group on asymptotically hyperbolic manifolds. J. Funct. Anal., 184(2):291-312, 2001.
• [7] Antônio Sá Barreto. The wave group and radiation fields on asymptotically hyperbolic manifolds. In Séminaire: Équations aux Dérivées Partielles, 1999-2000, Sémin. Équ. Dériv. Partielles, pages Exp. No. XXIII, 13. École Polytech., Palaiseau, 2000.
• [8] Antônio Sá Barreto and Siu-Hung Tang. Existence of resonances in even dimensional potential scattering. Comm. Partial Differential Equations, 25(5-6):1143-1151, 2000.
• [9] Mark S. Joshi and Antônio Sá Barreto. Inverse scattering on asymptotically hyperbolic manifolds. Acta Math., 184(1):41-86, 2000.
• [10] Antônio Sá Barreto. Lower bounds for the number of resonances in even-dimensional potential scattering. J. Funct. Anal., 169(1):314-323, 1999.
• [11] Mark S. Joshi and Antônio Sá Barreto. Determining asymptotics of magnetic fields from fixed energy scattering data. Asymptot. Anal., 21(1):61-70, 1999.
• [12] Mark S. Joshi and Antônio Sá Barreto. Recovering asymptotics of metrics from fixed energy scattering data. Invent. Math., 137(1):127-143, 1999.
• [13] Antônio Sá Barreto and Siu-Hung Tang. Existence of resonances in metric scattering. Comput. Appl. Math., 17(1):3-18, 1998.
• [14] Mark S. Joshi and Antônio Sá Barreto. The generation of semilinear singularities by a swallowtail caustic. Amer. J. Math., 120(3):529-550, 1998.
• [15] Mark S. Joshi and Antônio Sá Barreto. Recovering asymptotics of short range potentials. Comm. Math. Phys., 193(1):197-208, 1998.
• [16] Antônio Sá Barreto and Maciej Zworski. Distribution of resonances for spherical black holes. Math. Res. Lett., 4(1):103-121, 1997.
• [17] Richard B. Melrose, Antônio Sá Barreto, and Maciej Zworski. Semi-linear diffraction of conormal waves. Astérisque, (240):vi+132 pp. (1997), 1996.
• [18] Antônio Sá Barreto and Maciej Zworski. Existence of resonances in potential scattering. Comm. Pure Appl. Math., 49(12):1271-1280, 1996.
• [19] Rodrigo Bañuelos and Antônio Sá Barreto. On the heat trace of Schrödinger operators. Comm. Partial Differential Equations, 20(11-12):2153-2164, 1995.
• [20] Antônio Sá Barreto and Maciej Zworski. Existence of resonances in three dimensions. Comm. Math. Phys., 173(2):401-415, 1995.
• [21] Richard B. Melrose and Antônio Sá Barreto. Non-linear interaction of a cusp and a plane. Comm. Partial Differential Equations, 20(5-6):961-1032, 1995.
• [22] Antônio Sá Barreto. Evolution of semilinear waves with swallowtail singularities. Duke Math. J., 75(3):645-710, 1994.
• [23] Antônio Sá Barreto. Second microlocal ellipticity and propagation of conormality for semilinear wave equations. J. Funct. Anal., 102(1):47-71, 1991.
• [24] Antônio Sá Barreto. Evolution of semilinear conormal waves. In Journées “Équations aux Dérivées Partielles” (Saint Jean de Monts, 1991), pages Exp.No.XII, 18. École Polytech., Palaiseau, 1991.
• [25] Antônio Sá Barreto. On the interactions of conormal waves for semilinear wave equations. In Microlocal analysis and nonlinear waves (Minneapolis, MN, 1988-1989), volume 30 of IMA Vol. Math. Appl., pages 1-7. Springer, New York, 1991.
• [26] Antônio Sá Barreto. Interactions of conormal waves for fully semilinear wave equations. J. Funct. Anal., 89(2):233-273, 1990.
• [27] Antônio Sá Barreto and Richard B. Melrose. Examples of nondiscreteness for the interaction geometry of semilinear progressing waves in two space dimensions. In Partial differential equations (Rio de Janeiro, 1986), volume 1324 of Lecture Notes in Math., pages 186-196. Springer, Berlin, 1988.