@article{SEDP_1999-2000____A22_0,
author = {S\'a Barreto, Ant\^onio},
title = {The {Wave} {Group} and {Radiation} {Fields} on {Asymptotically} {Hyperbolic} {Manifolds}},
journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
note = {talk:22},
pages = {1--11},
publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {1999-2000},
zbl = {1061.58023},
language = {en},
url = {http://archive.numdam.org/item/SEDP_1999-2000____A22_0/}
}
TY - JOUR AU - Sá Barreto, Antônio TI - The Wave Group and Radiation Fields on Asymptotically Hyperbolic Manifolds JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:22 PY - 1999-2000 SP - 1 EP - 11 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://archive.numdam.org/item/SEDP_1999-2000____A22_0/ LA - en ID - SEDP_1999-2000____A22_0 ER -
%0 Journal Article %A Sá Barreto, Antônio %T The Wave Group and Radiation Fields on Asymptotically Hyperbolic Manifolds %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:22 %D 1999-2000 %P 1-11 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://archive.numdam.org/item/SEDP_1999-2000____A22_0/ %G en %F SEDP_1999-2000____A22_0
Sá Barreto, Antônio. The Wave Group and Radiation Fields on Asymptotically Hyperbolic Manifolds. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1999-2000), Exposé no. 22, 11 p. http://archive.numdam.org/item/SEDP_1999-2000____A22_0/
[1] S. Agmon, A representation theorem for solutions of Schrödinger type equations on non-compact Riemannian manifolds. Astérisque 210 Vol. 2, 13-26, (1992). | Numdam | MR | Zbl
[2] L. Andersson, P.T. Chrusciel, H. Friedrich, On the regularity of solutions to the Yamabe problem and the existence of smooth hyperboloidal initial data for Einstein’s field equations. Comm. Math. Phys. 149, 587-612, (1992). | Zbl
[3] D. Borthwick, P. Perry, Scattering poles for asymptotically hyperbolic manifolds. Preprint, 1999. | MR
[4] J. Chazarin. Formule de Poisson pour les varietés Riemanniennes. Inventiones Math. 24, 65-82 (1974). | MR | Zbl
[5] T. Christiansen. Scattering theory for manifolds with cylindrical ends. J. Funct. Anal. 131, 499-530 (1995). | MR | Zbl
[6] T. Christiansen. Weyl asymptotics for the Laplacian on asymptotically Euclidean spaces. American J. of Math. 121, 1-22 (1999). | MR | Zbl
[7] J. Duistermaat, V.W. Guillemin, The spectrum of positive elliptic operators and periodic bicharacteristics. Inventiones mathematicae 29, 39-79 (1975). | MR | Zbl
[8] J. Duistermaat, L Hörmander, Fourier integral operators II. Acta Mathematica 128, 184-269 (1972). | MR | Zbl
[9] C.R. Graham, Volume and area renormalization for conformally compact Eistein metrics. Preprint 1999. | MR
[10] F.G. Friedlander, Radiation fields and hyperbolic scattering theory. Math. Proc. Camb. Phil. Soc. 88, 483-515, (1980). | MR | Zbl
[11] F.G. Friedlander, Notes on the wave equation on asymptotically Euclidean manifolds. To appear in J. of Functional Analysis. | MR | Zbl
[12] L. Guillopé, M. Zworski, Scattering asymptotics for Riemann surfaces. Ann. of Math. 145, 597-660, (1997). | MR | Zbl
[13] L. Guillopé, M. Zworski, The wave trace for Riemann surfaces. GAFA, Geom. Func. Anal. 9, 1156-1168, (1999). | MR | Zbl
[14] S. Helgason, Wave equations on homogeneous spaces. Lecture Notes in Math., 1077, 254-287 (1984). | MR | Zbl
[15] L. Hörmander, Fourier integral operators I. Acta Mathematica 127, 79-183, (1971). | MR | Zbl
[16] L. Hörmander, The spectral function of an elliptic operator. Acta Mathematica 121, 193-218, (1968). | MR | Zbl
[17] L. Hörmander, The analysis of Partial Differential Operators. Vol 3. Springer Verlag, 1985. | Zbl
[18] M.S. Joshi, A. Sá Barreto, Inverse scattering on asymptotically hyperbolic manifolds. Acta Mathematica 184 41-86, 2000. | MR | Zbl
[19] M.S. Joshi, A. Sá Barreto, The wave group on asymptotically hyperbolic manifolds. Preprint, 2000. | MR | Zbl
[20] L.A. Kiprijanov, L.A. Ivanov, The Euler-Poisson equation in a Riemannian space. Soviet Math. Dokl. 24 No. 2 331-335 (1981). | Zbl
[21] P. Lax, R. Phillips, Scattering theory for automorphic forms. Ann. of Math. Studies No. 87 Princeton Univ Press, 1976. | MR | Zbl
[22] R. Mazzeo, The Hodge cohomology of a conformally compact metric. Journ. Diff. Geom. 28 (1988) 309-339. | MR | Zbl
[23] R. Mazzeo, Elliptic theory of differential edge operators I. Comm. PDE 16 (1991), 1615-1664. | MR | Zbl
[24] R. Mazzeo, R.B. Melrose, Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature. Journal of Functional Analysis, 75, No 2, (1987), 260-310. | MR | Zbl
[25] R.B. Melrose, Transformation of boundary value problems. Acta Mathematica, 147 (1981) no 3–4, 149–236. | MR | Zbl
[26] R.B. Melrose, Differential Analysis on Manifolds with Corners. To appear.
[27] R.B. Melrose, Spectral and Scattering Theory for the Laplacian on Asymptotically Euclidean Spaces. Spectral and Scattering Theory, (M. Ikawa, ed.), Marcel Dekker, 1994. | MR | Zbl
[28] R.B Melrose, Geometric scattering theory. Cambridge University Press, 1995. | MR | Zbl
[29] R.B. Melrose, The Atiyah-Patodi-Singer Index Theorem. A.K. Peters, Wellesley, MA, 1993. | MR | Zbl
[30] R. B. Melrose and A. Sá Barreto, Non-linear interaction of a cusp and a plane. Comm. in P.D.E, 20 (5 & 6), 961-1032 (1995). | MR | Zbl
[31] A. Sá Barreto, M. Zworski, Distribution of resonances for spherical black holes. Math. Res. Letters 4, 103-121 (1997). | MR | Zbl
[32] A. Sá Barreto, Radiation fields for asymptotically hyperbolic manifolds. In preparation.
[33] R. Seeley, Complex powers of elliptic operators. Singular Integrals. Proc. Sympos. Pure Math. Amer. Math. Soc., Providence, R.I 288-307, 1967. | MR | Zbl
