The Wave Group and Radiation Fields on Asymptotically Hyperbolic Manifolds
- [1] Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A.
Séminaire Équations aux dérivées partielles (1999-2000)
- Volume: 1999-2000, page 1-11
Access Full Article
topHow to cite
topSá Barreto, Antônio. "The Wave Group and Radiation Fields on Asymptotically Hyperbolic Manifolds." Séminaire Équations aux dérivées partielles 1999-2000 (1999-2000): 1-11. <http://eudml.org/doc/10997>.
@article{SáBarreto1999-2000,
affiliation = {Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A.},
author = {Sá Barreto, Antônio},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-11},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {The Wave Group and Radiation Fields on Asymptotically Hyperbolic Manifolds},
url = {http://eudml.org/doc/10997},
volume = {1999-2000},
year = {1999-2000},
}
TY - JOUR
AU - Sá Barreto, Antônio
TI - The Wave Group and Radiation Fields on Asymptotically Hyperbolic Manifolds
JO - Séminaire Équations aux dérivées partielles
PY - 1999-2000
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 1999-2000
SP - 1
EP - 11
LA - eng
UR - http://eudml.org/doc/10997
ER -
References
top- S. Agmon, A representation theorem for solutions of Schrödinger type equations on non-compact Riemannian manifolds. Astérisque 210 Vol. 2, 13-26, (1992). Zbl0791.58104MR1221349
- 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). Zbl0764.53027
- D. Borthwick, P. Perry, Scattering poles for asymptotically hyperbolic manifolds. Preprint, 1999. Zbl1009.58021MR1867379
- J. Chazarin. Formule de Poisson pour les varietés Riemanniennes. Inventiones Math. 24, 65-82 (1974). Zbl0281.35028MR343320
- T. Christiansen. Scattering theory for manifolds with cylindrical ends. J. Funct. Anal. 131, 499-530 (1995). Zbl0837.58034MR1345040
- T. Christiansen. Weyl asymptotics for the Laplacian on asymptotically Euclidean spaces. American J. of Math. 121, 1-22 (1999). Zbl0924.58006MR1704995
- J. Duistermaat, V.W. Guillemin, The spectrum of positive elliptic operators and periodic bicharacteristics. Inventiones mathematicae 29, 39-79 (1975). Zbl0307.35071MR405514
- J. Duistermaat, L Hörmander, Fourier integral operators II. Acta Mathematica 128, 184-269 (1972). Zbl0232.47055MR388464
- C.R. Graham, Volume and area renormalization for conformally compact Eistein metrics. Preprint 1999. MR1758076
- F.G. Friedlander, Radiation fields and hyperbolic scattering theory. Math. Proc. Camb. Phil. Soc. 88, 483-515, (1980). Zbl0465.35068MR583989
- F.G. Friedlander, Notes on the wave equation on asymptotically Euclidean manifolds. To appear in J. of Functional Analysis. Zbl0997.58013MR1846782
- L. Guillopé, M. Zworski, Scattering asymptotics for Riemann surfaces. Ann. of Math. 145, 597-660, (1997). Zbl0898.58054MR1454705
- L. Guillopé, M. Zworski, The wave trace for Riemann surfaces. GAFA, Geom. Func. Anal. 9, 1156-1168, (1999). Zbl0947.58022MR1736931
- S. Helgason, Wave equations on homogeneous spaces. Lecture Notes in Math., 1077, 254-287 (1984). Zbl0547.58037MR765556
- L. Hörmander, Fourier integral operators I. Acta Mathematica 127, 79-183, (1971). Zbl0212.46601MR388463
- L. Hörmander, The spectral function of an elliptic operator. Acta Mathematica 121, 193-218, (1968). Zbl0164.13201MR609014
- L. Hörmander, The analysis of Partial Differential Operators. Vol 3. Springer Verlag, 1985. Zbl0601.35001
- M.S. Joshi, A. Sá Barreto, Inverse scattering on asymptotically hyperbolic manifolds. Acta Mathematica 184 41-86, 2000. Zbl1142.58309MR1756569
- M.S. Joshi, A. Sá Barreto, The wave group on asymptotically hyperbolic manifolds. Preprint, 2000. Zbl0997.58010MR1851000
- L.A. Kiprijanov, L.A. Ivanov, The Euler-Poisson equation in a Riemannian space. Soviet Math. Dokl. 24 No. 2 331-335 (1981). Zbl0488.35065
- P. Lax, R. Phillips, Scattering theory for automorphic forms. Ann. of Math. Studies No. 87 Princeton Univ Press, 1976. Zbl0362.10022MR562288
- R. Mazzeo, The Hodge cohomology of a conformally compact metric. Journ. Diff. Geom. 28 (1988) 309-339. Zbl0656.53042MR961517
- R. Mazzeo, Elliptic theory of differential edge operators I. Comm. PDE 16 (1991), 1615-1664. Zbl0745.58045MR1133743
- 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. Zbl0636.58034MR916753
- R.B. Melrose, Transformation of boundary value problems. Acta Mathematica, 147 (1981) no 3–4, 149–236. Zbl0492.58023MR639039
- R.B. Melrose, Differential Analysis on Manifolds with Corners. To appear. Zbl0754.58035
- R.B. Melrose, Spectral and Scattering Theory for the Laplacian on Asymptotically Euclidean Spaces. Spectral and Scattering Theory, (M. Ikawa, ed.), Marcel Dekker, 1994. Zbl0837.35107MR1291640
- R.B Melrose, Geometric scattering theory. Cambridge University Press, 1995. Zbl0849.58071MR1350074
- R.B. Melrose, The Atiyah-Patodi-Singer Index Theorem. A.K. Peters, Wellesley, MA, 1993. Zbl0796.58050MR1348401
- 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). Zbl0847.35086MR1326913
- A. Sá Barreto, M. Zworski, Distribution of resonances for spherical black holes. Math. Res. Letters 4, 103-121 (1997). Zbl0883.35120MR1432814
- A. Sá Barreto, Radiation fields for asymptotically hyperbolic manifolds. In preparation. Zbl1154.58310
- R. Seeley, Complex powers of elliptic operators. Singular Integrals. Proc. Sympos. Pure Math. Amer. Math. Soc., Providence, R.I 288-307, 1967. Zbl0159.15504MR237943
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.