Spectral and scattering theory for symbolic potentials of order zero

Andrew Hassell; Richard Melrose; András Vasy

Séminaire Équations aux dérivées partielles (2000-2001)

  • Volume: 2000-2001, page 1-19

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Hassell, Andrew, Melrose, Richard, and Vasy, András. "Spectral and scattering theory for symbolic potentials of order zero." Séminaire Équations aux dérivées partielles 2000-2001 (2000-2001): 1-19. <http://eudml.org/doc/11009>.

@article{Hassell2000-2001,
author = {Hassell, Andrew, Melrose, Richard, Vasy, András},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {Schrödinger operator; generalized eigenfunctions; scattering matrix; scattering metric; Fourier integral operator},
language = {eng},
pages = {1-19},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Spectral and scattering theory for symbolic potentials of order zero},
url = {http://eudml.org/doc/11009},
volume = {2000-2001},
year = {2000-2001},
}

TY - JOUR
AU - Hassell, Andrew
AU - Melrose, Richard
AU - Vasy, András
TI - Spectral and scattering theory for symbolic potentials of order zero
JO - Séminaire Équations aux dérivées partielles
PY - 2000-2001
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2000-2001
SP - 1
EP - 19
LA - eng
KW - Schrödinger operator; generalized eigenfunctions; scattering matrix; scattering metric; Fourier integral operator
UR - http://eudml.org/doc/11009
ER -

References

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  2. J. Brüning and V.W. Guillemin (Editors), Fourier integral operators, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1994. Zbl0791.47043MR1287873
  3. J.J. Duistermaat and L. Hörmander, Fourier integral operators, II, Acta Math. 128 (1972), 183–269. Zbl0232.47055MR388464
  4. V.W. Guillemin and D. Schaeffer, On a certain class of Fuchsian partial differential equations., Duke Math. J., 4 (1977), 157–199. Zbl0356.35080MR430499
  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. Zbl1141.81029
  6. Ira W. Herbst, Spectral and scattering theory fo Schrödinger operators with potentials independent of | x | , Amer. J. Math. 113 (1991), 509–565. Zbl0732.35063MR1109349
  7. L. Hörmander, Fourier integral operators, I, Acta Math. 127 (1971), 79–183, See also [2]. Zbl0212.46601MR388463
  8. —, The Weyl calculus of pseudo-differential operators, Comm. Pure Appl. Math. 32 (1979), 359–443. Zbl0388.47032
  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. Zbl0837.35107MR1291640
  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. Zbl0853.35142MR1380979
  11. R.B. Melrose and M. Zworski, Scattering metrics and geodesic flow at infinity, Invent. Math. 124 (1996), 389–436. Zbl0855.58058MR1369423
  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. Zbl0599.35139MR801291
  13. M.A. Shubin, Pseudodifferential operators on ℝ n , Sov. Math. Dokl. 12 (1971), 147-151. Zbl0249.47043

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