Spectral and scattering theory for symbolic potentials of order zero
Séminaire Équations aux dérivées partielles (Polytechnique) (2000-2001), Talk no. 13, 19 p.
@article{SEDP_2000-2001____A13_0,
author = {Hassell, Andrew and Melrose, Richard and Vasy, Andr\'as},
title = {Spectral and scattering theory for symbolic potentials of order zero},
journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2000-2001},
note = {talk:13},
mrnumber = {2020655},
zbl = {1063.35126},
language = {en},
url = {http://www.numdam.org/item/SEDP_2000-2001____A13_0}
}

Hassell, Andrew; Melrose, Richard; Vasy, András. Spectral and scattering theory for symbolic potentials of order zero. Séminaire Équations aux dérivées partielles (Polytechnique) (2000-2001), Talk no. 13, 19 p. http://www.numdam.org/item/SEDP_2000-2001____A13_0/

[1] Shmuel Agmon, Jaime Cruz, and Ira Herbst, Generalized Fourier transform for Schrödinger operators with potentials of order zero, J. Funct. Anal. 167 (1999), 345–369. | MR 1716200 | Zbl 0937.35033

[2] J. Brüning and V.W. Guillemin (Editors), Fourier integral operators, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1994. | MR 1287874 | MR 1287873

[3] J.J. Duistermaat and L. Hörmander, Fourier integral operators, II, Acta Math. 128 (1972), 183–269. | MR 388464 | Zbl 0232.47055

[4] V.W. Guillemin and D. Schaeffer, On a certain class of Fuchsian partial differential equations., Duke Math. J., 4 (1977), 157–199. | MR 430499 | Zbl 0356.35080

[5] Ira Herbst and Erik Skibsted, Quantum scattering for homogeneous of degree zero potentials: Absence of channels at local maxima and saddle points, Tech. report, Center for Mathematical Physics and Stochastics, 1999.

[6] Ira W. Herbst, Spectral and scattering theory fo Schrödinger operators with potentials independent of $|x|$, Amer. J. Math. 113 (1991), 509–565. | MR 1109349 | Zbl 0732.35063

[7] L. Hörmander, Fourier integral operators, I, Acta Math. 127 (1971), 79–183, See also [2]. | MR 388463 | Zbl 0212.46601

[8] —, The Weyl calculus of pseudo-differential operators, Comm. Pure Appl. Math. 32 (1979), 359–443. | Zbl 0388.47032

[9] R.B. Melrose, Spectral and scattering theory for the Laplacian on asymptotically Euclidian spaces, Spectral and scattering theory (Sanda, 1992) (M. Ikawa, ed.), Marcel Dekker, 1994, pp. 85–130. | MR 1291640 | Zbl 0837.35107

[10] —, Fibrations, compactifications and algebras of pseudodifferential operators, Partial Differential Equations and Mathematical Physics. The Danish-Swedish Analysis Seminar, 1995 (Lars Hörmander and Anders Melin, eds.), Birkhäuser, 1996, pp. 246–261. | MR 1380979 | Zbl 0853.35142

[11] R.B. Melrose and M. Zworski, Scattering metrics and geodesic flow at infinity, Invent. Math. 124 (1996), 389–436. | MR 1369423 | Zbl 0855.58058

[12] Richard B. Melrose, The wave equation for a hypoelliptic operator with symplectic characteristics of codimension two, J. Analyse Math. 44 (1984/85), 134–182. MR 87e:58199. | MR 801291 | Zbl 0599.35139

[13] M.A. Shubin, Pseudodifferential operators on ${ℝ}^{n}$, Sov. Math. Dokl. 12 (1971), 147-151. | Zbl 0249.47043