journal article Dec 01, 1998

Scattering theory for perturbed stratified media

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References
47
[1]
S. Agmon,Spectral theory of Schrödinger operators on Euclidean and on non-Euclidean spaces, Comm. Pure Appl. Math.39 (1986), S3-S16. 10.1002/cpa.3160390703
[2]
C. Bardos, J.-C. Guillot and J. V. Ralston,La relation de Poisson pour l’équation des ondes dans un ouvert non borné. Application à la théorie de la diffusion, Comm. Partial Differential Equations7 (1982), 905–958. 10.1080/03605308208820241
[3]
M. Ben-Artzi, Y. Dermenjian and J.-C. Guillot,Acoustic waves in perturbed stratified fluids: a spectral theory, Comm. Partial Differential Equations14 (4) (1989), 479–517. 10.1080/03605302.1989.12088446
[4]
M. Sh. Birman and M. G. Krein,On the theory of wave operators and scattering operators, Dokl. Akad. Nauk SSSR144 (1962), 475–478.
[5]
N. Bleistein and R. A. Hendelsman,Asymptotic Expansions of Integrals, Holt, Rinehart and Winston, New York, 1975.
[6]
A. Boutet de Monvel-Berthier and D. Manda,Spectral and scattering theory for wave propagation in perturbed stratified media, J. Math. Anal. Appl.191 (1995), 137–167. 10.1016/s0022-247x(85)71124-9
[7]
V. S. Buslaev,Trace formulas for the Schrödinger operators in a three-dimensional space, Dokl. Akad. Nauk SSSR143 (1962), 1067–1070.
[8]
T. Christiansen,Scattering theory for manifolds with asymptotically cylindrical ends, J. Funct. Anal.131 (2) (1995), 499–530. 10.1006/jfan.1995.1097
[9]
S. DeBièvre and D. W. Pravica,Spectral analysis for optical fibres and stratified fluids I: The limiting absorption principle, J. Funct. Anal.98 (1991), 404–436. 10.1016/0022-1236(91)90085-j
[10]
S. DeBièvre and D. W. Pravica,Spectral analysis for optical fibres and stratified fluids II: Absence of eigenvalues, Comm. Partial Differential Equations17 (1&2) (1992), 69–97. 10.1080/03605309208820835
[11]
P. Deift and E. Trubowitz,Inverse scattering on the line, Comm. Pure Appl. Math.32 (1979), 121–251. 10.1002/cpa.3160320202
[12]
Y. Dermenjian and J.-C. Guillot,Théorie spectrale de la propagation des ondes acoustiques dans un milieu stratifié perturbé, J. Differential Equations62 (3) (1986), 357–409. 10.1016/0022-0396(86)90091-4
[13]
J. J. Duistermaat and V. Guillemin,The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math.29 (1975), 39–79. 10.1007/bf01405172
[14]
D. Eidus,The limiting absorption and amplitude principles for the diffraction problem with two unbounded media, Comm. Math. Phys.107 (1986), 29–38. 10.1007/bf01206952
[15]
I. S. Gradshteyn and I. M. Ryzik, eds.,Table of Integrals, Series, and Products, Academic Press, New York, 1994.
[16]
L. Guillopé and M. Zworski,Scattering asymptotics for Riemann surfaces, Ann. of Math. (2)145 (1997), 597–660. 10.2307/2951846
[17]
L. Hörmander,The spectral function of an elliptic operator, Acta Math.121 (1968), 193–218. 10.1007/bf02391913
[18]
L. Hörmander,The Analysis of Linear Partial Differential Operators III, Springer-Verlag, New York, 1990. 10.1007/978-3-642-61497-2
[19]
H. Isozaki,Asymptotic properties of generalized eigenfunctions for three body Schrödinger operators, Comm. Math. Phys.153 (1993), 1–21. 10.1007/bf02099038
[20]
H. Isozaki,Inverse scattering theory for wave equations in stratified media, J. Differential Equations138 (1997), no. 1, 19–54. 10.1006/jdeq.1997.3271
[21]
D. S. Jones,The Theory of Electromagnetism, Macmillan, New York, 1964.
[22]
P. Lax and R. Phillips,Scattering Theory, Academic Press, New York, 1967.
[23]
P. Lax and R. Phillips,Scattering Theory for Automorphic Functions, Ann. of Math. Studies,87, Princeton University Press, Princeton, N.J., 1976.
[24]
R. B. Melrose,Geometric Scattering Theory, Cambridge University Press, Cambridge, 1995.
[25]
R. B. Melrose,The Atiyah—Patodi—Singer Index Theorem, A. K. Peters, Wellesley, MA, 1993. 10.1201/9781439864609
[26]
R. B. Melrose,Weyl asymptotics for the phase in obstacle scattering, Comm. Partial Differential Equations13 (1988), 1431–1439. 10.1080/03605308808820582
[27]
R. B. Melrose,Spectral and scattering theory for the Laplacian on asymptotically Euclidian spaces, inSpectral and Scattering Theory (M. Ikawa, ed.), Marcel Dekker, New York, 1994, pp. 85–130.
[28]
R. B. Melrose,Differential Analysis on Manifolds with Corners, in preparation.
[29]
W. Müller,Spectral geometry and scattering theory for certain complete surfaces of finite volume, Invent. Math.109 (1992), 265–305. 10.1007/bf01232028
[30]
F. Odeh,Uniqueness theorems for the Helmholtz equation in domain with infinite boundaries, J. Math. Mech.12 (6) (1963), 857–867.
[31]
M. Petry,Acoustic scattering in a layered medium, inInverse Scattering and Potential Problems in Mathematical Physics (R. Kleinman, R. Kress and E. Martensen, eds.), Peter Lang, Frankfort, 1995, pp. 141–156.
[32]
J. Ralston,Propagation of singularities and the scattering matrix, inSingularities in Boundary Value Problems, Proc. NATO Adv. Study Inst., Maratea, 1980, D. Reidel, Dordrecht, Boston, 1981, pp. 169–184. 10.1007/978-94-009-8434-9_8
[33]
M. Reed and B. Simon,Methods of Modern Mathematical Physics: Volume III, Scattering Theory, Academic Press, New York, 1979.
[34]
G. F. Roach and B. Zhang,On Sommerfeld radiation conditions for the diffraction problem with two unbounded media, Proc. Roy. Soc. Edinburgh Sect. A121A (1992), 149–161. 10.1017/s0308210500014190
[35]
D. Robert,Asymptotique à grande énergie de la phase de diffusion pour un potentiel, Asymptotic Anal. 3 (1991), 301–320. 10.3233/asy-1991-3403
[36]
D. Robert,Asymptotique de la phase de diffusion à haute énergie pour des perturbations du second ordre du laplacien, Ann. Sci. école Norm. Sup. (4)25 (1992), 107–134. 10.24033/asens.1645
[37]
D. Robert,A trace formula for obstacle problems and applications, inMathematical Results in Quantum Mechanics (Blossin, 1993), Operator Theory: Advances and Applications, Vol. 70, BirkhÄuser, Basel, 1994, pp. 283–292. 10.1007/978-3-0348-8545-4_34
[38]
M. Taylor,Partial Differential Equations II: Qualitative Studies of Linear Equations, Springer-Verlag, New York, 1996. 10.1007/978-1-4757-4187-2
[39]
Structure of the resolvent for three-body potentials

András Vasy

Duke Mathematical Journal 1997 10.1215/s0012-7094-97-09010-4
[40]
A. Vasy,Asymptotic behaviour of generalized eigenfunctions in n-body scattering, J. Funct. Anal.148 (1997), no. 1, 170–184. 10.1006/jfan.1996.3053
[41]
A. Vasy,Propagation of singularities in three-body scattering, Ph.D. thesis, M.I.T., 1997.
[42]
R. Weder,Spectral and Scattering Theory for Wave Propagation in Perturbed Stratified Media, Springer-Verlag, New York, 1991. 10.1007/978-1-4612-4430-1
[43]
C. Wilcox,Sound Propagation in Stratified Fluids, Springer-Verlag, New York, 1984. 10.1007/978-1-4612-1124-2
[44]
Y. Xu,Scattering of acoustic waves by an obstacle in a stratified medium, inPartial Differential Equations with Real Analysis (H. Begehr and A. Jeffrey, eds.), Pitman Research Notes in Mathematics, # 263, Longman Scientific and Technical, Harlow, UK, 1992, pp. 147–168.
[45]
Y. Xu,Reciprocity relations and completeness of far-field pattern vectors for obstacle scattering of acoustic wave in a stratified medium, Math. Methods Appl. Sci.18 (1995), 51–66. 10.1002/mma.1670180104
[46]
Y. Xu,Radiation condition and scattering problem for time-harmonic acoustic waves in a stratified medium with a nonstratified inhomogeneity, IMA J. Appl. Math.54 (1995), 9–29. 10.1093/imamat/54.1.9
[47]
D. R. Yafaev,Mathematical Scattering Theory, American Mathematical Society, Providence, Rhode Island, 1992. 10.1090/mmono/105
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Published
Dec 01, 1998
Vol/Issue
76(1)
Pages
1-43
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Cite This Article
T. Christiansen (1998). Scattering theory for perturbed stratified media. Journal d'Analyse Mathématique, 76(1), 1-43. https://doi.org/10.1007/bf02786928
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