Pacific Journal of Mathematics

A remark on the limiting absorption principle for the reduced wave equation with two unbounded media.

Yoshimi Saitō

Article information

Source
Pacific J. Math., Volume 136, Number 1 (1989), 183-208.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102650851

Mathematical Reviews number (MathSciNet)
MR971942

Zentralblatt MATH identifier
0705.35028

Subjects
Primary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx]
Secondary: 35P25: Scattering theory [See also 47A40]

Citation

Saitō, Yoshimi. A remark on the limiting absorption principle for the reduced wave equation with two unbounded media. Pacific J. Math. 136 (1989), no. 1, 183--208. https://projecteuclid.org/euclid.pjm/1102650851


Export citation

References

  • [I] S. Agmon, Spectralproperties of Schrdingeroperators and scattering theory, Ann. Scoula Nor.Sup.Pisa, (4) 2 (1975), 151-218.
  • [2] A. Devinatz and P. Rejto, A limiting absorption principle for Schrdinger op- erators with oscillating potentials. I, II, J. Diff. Equations, 49 (1983), 29-84, 85-104.
  • [3] M. S. P. Eastham and H. Kalf, Schrdinger-TypeOperators WithContinuous Spectra, Pitman, London, 1982.
  • [4] D. Eidus, The limiting absorption and amplitude principles for thediffraction problem with two unbounded media, Comm. Math. Phys., 107 (1986), 29-38.
  • [5] T. Ikebe and Y. Sait, Limiting absorption method and absolute continuity for the Schrdinger operator,J. Kyoto Univ., 7 (1972), 513-542.
  • [6] W. Jager, Ein gewhnlicher Differentialoperator zweiter Ordnungfur Funktionen mit Wertenin einem Hilbertraum,Math. Z., 113 (1970), 68-98.
  • [7] T. Kato, Growth properties of solutions of the reduced wave equation with a variablecoefficient, Comm. Pure Appl. Math., 12 (1959), 403-425.
  • [8] R. Lavine, Absolute continuity of positive spectrum for Schrdinger operators with long-rangepotentials, J. Funct. Anal., 12 (1973), 30-54.
  • [9] K. Mochizuki and J. Uchiyama, Radiation conditions and spectral theory for 2-bodySchrdinger operatorswith "oscillatory'' long-range potentials, I. J.Math. Kyoto Univ., 18 (1978), 377-408.
  • [10] Y. Saito, The principle of limiting absorptionfor second-order differential equa- tions with operator-valued coefficients,Publ. Res. Inst. Math. Sci. Kyoto Univ., 7(1972/72), 581-619.
  • [II] Y. Saito, Spectral representationsfor Schrdingeroperators with long-range po- tentials, Lecture Notes in Mathematics 727, Springer, Berlin-Heidelberg-New York, 1979.
  • [12] Y. Saito, Schrdinger operators with nonspherical radiation condition, Pacific J. Math., 126(1987), 331-359.