## Scattering theory for hyperbolic systems with coefficients of Gevrey type

HTML articles powered by AMS MathViewer

- by William L. Goodhue PDF
- Trans. Amer. Math. Soc.
**180**(1973), 337-346 Request permission

## Abstract:

Using the techniques developed by P. D. Lax and R. S. Phillips, qualitative results on the location of the poles of the scattering matrix for symmetric, hyperbolic systems are obtained. The restrictions placed on the system are that the coefficient matrices be of Gevrey type and that the bicharacteristic rays tend to infinity.## References

- R. Courant and P. D. Lax,
*The propagation of discontinuities in wave motion*, Proc. Nat. Acad. Sci. U.S.A.**42**(1956), 872–876. MR**81420**, DOI 10.1073/pnas.42.11.872 - Avner Friedman,
*Regularity of fundamental solutions of hyperbolic equations*, Arch. Rational Mech. Anal.**11**(1962), 62–96. MR**144076**, DOI 10.1007/BF00253930
W. L. Goodhue, - William L. Goodhue,
*On the regularity of the Riemann function for hyperbolic equations*, Trans. Amer. Math. Soc.**175**(1973), 483–490. MR**318685**, DOI 10.1090/S0002-9947-1973-0318685-5 - Einar Hille and Ralph S. Phillips,
*Functional analysis and semi-groups*, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, R.I., 1957. rev. ed. MR**0089373** - Peter D. Lax and Ralph S. Phillips,
*Scattering theory*, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR**0217440** - P. D. Lax and R. S. Phillips,
*The acoustic equation with an indefinite energy form and the Schrödinger equation*, J. Functional Analysis**1**(1967), 37–83. MR**0217441**, DOI 10.1016/0022-1236(67)90026-2 - J.-L. Lions and E. Magenes,
*Problèmes aux limites non homogènes et applications. Vol. 3*, Travaux et Recherches Mathématiques, No. 20, Dunod, Paris, 1970 (French). MR**0291887**
D. Ludwig,

*On the location of the poles of the scattering matrix for symmetric hyperbolic equations*, Thesis, New York University, October 1971.

*Lecture notes on scattering theory*, Rocky Mountain Regional Summer Math. Seminar, Flagstaff, Arizona, 1969.

*Exact and asymptotic solutions of the Cauchy problem*, Report NYO-2545, Atomic Energy Commission Research and Development.

## Additional Information

- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**180**(1973), 337-346 - MSC: Primary 35P25
- DOI: https://doi.org/10.1090/S0002-9947-1973-0415094-5
- MathSciNet review: 0415094