<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet type="text/xsl" href="f1.xsl"?>
<top_article>
 <mrnumber>MR1454464</mrnumber>
 <author>Shimizu, Senjo</author>
 <author_utf8>Senjo SHIMIZU</author_utf8>
 <title>Scattering theory for elastic wave propagation problems in               perturbed stratified media $R^3$</title>
 <journal>Funkcialaj Ekvacioj. Serio Internacia</journal>
 <volume>40</volume>
 <year>1997</year>
 <page>57--77</page>
 <url_pdf>http://fe.math.kobe-u.ac.jp/FE/Free/vol40/fe40-1-4.pdf</url_pdf>
 <url_infty_pdf>http://fe.math.kobe-u.ac.jp/FE/FE_pdf_with_bookmark/FE35-40-en_KML/fe40-057-077/fe40-057-077.pdf</url_infty_pdf>
 <mathsci_link> http://www.ams.org/mathscinet-getitem?mr=MR1454464</mathsci_link>
<fesi_info>
  <FILE>fe40-057-077</FILE>
  <YEAR>1997</YEAR>
  <TITLE>Scattering Theory for Elastic Wave Propagation Problems in Perturbed Stratified Media $R^3$</TITLE>
  <AUTHOR>SHIMIZU, Senjo</AUTHOR>
  <AUTHOR_utf8>Senjo SHIMIZU</AUTHOR_utf8>
</fesi_info>

<references>
  <article>
    <bibitem>Bi</bibitem>
    <author>Belopolskii, A. L.; Birman, M. &#352;.</author>
    <title>The existence of wave operators in the theory of scattering with a pair of spaces</title>
    <journal>Izv. Acad. Nauk SSSR Ser. Mat.</journal>
    <ser>Mat</ser>
    <vol>32</vol>
    <year>1968</year>
    <page>1162-1175</page>
    <mr>MR0238101</mr>
    <score>91</score>
    <query_string>Cache/Bi/Birman,scattering,Izv*,1968,1969</query_string>
  </article>

  <article>
    <bibitem>D-G</bibitem>
    <author>Dermenjian, Y.; Guillot, J. C.</author>
    <title>Scattering of elastic waves in a perturbed isotropic half space with a free boundary. The limiting absorption principle</title>
    <journal>Math. Meth. in the Appl. Sci.</journal>
    <vol>10</vol>
    <year>1988</year>
    <page>87-124</page>
    <mr>MR0937415</mr>
    <score>100</score>
    <query_string>Cache/De/Dermenjian,Scattering,Math*,1988,1989</query_string>
  </article>

  <article>
    <bibitem>Gu</bibitem>
    <author>Guillot, J. C.</author>
    <title>Existence and uniqueness of a Rayleigh surface wave propagation along the free boundary of a transversely isotropic elastic half space</title>
    <journal>Math. Meth. in the Appl. Sci.</journal>
    <vol>8</vol>
    <year>1986</year>
    <page>289-310</page>
    <mr>MR0845932</mr>
    <score>95</score>
    <query_string>Cache/Gu/Guillot,transversely,Math*,1986,1987</query_string>
  </article>

  <article>
    <bibitem>Ik</bibitem>
    <author>Ikebe, T.</author>
    <title>Eigenfunction expansions associated with the Schr&#246;dinger operators and their applications to scattering theory</title>
    <journal>Arch. Rational Mech. Anal.</journal>
    <vol>5</vol>
    <year>1960</year>
    <page>1-34</page>
    <mr>MR0128355</mr>
    <score>92</score>
    <query_string>Cache/Ik/Ikebe,Eigenfunction,Arch*,1960,1961</query_string>
  </article>

  <article>
    <bibitem>It</bibitem>
    <author>Ito, H.</author>
    <title>Extended Korn's inequalities and the associated best possible constants</title>
    <journal>J. Elasticity</journal>
    <vol>24</vol>
    <year>1990</year>
    <page>43-78</page>
    <mr>MR1086253</mr>
    <score>100</score>
    <query_string>Cache/It/Ito,inequalities,J*,1990,1991</query_string>
  </article>

  <article>
    <bibitem>Ja</bibitem>
    <author>Jauch, J. M.</author>
    <title>Theory of scattering operator</title>
    <journal>Helv. Phys. Acta</journal>
    <vol>31</vol>
    <year>1958</year>
    <page>127-158</page>
    <mr>MR0094163</mr>
    <score>100</score>
    <query_string>Cache/Ja/Jauch,scattering,Helv*,1958,1959</query_string>
  </article>

  <article>
    <bibitem>Ka 1</bibitem>
    <author>Kato, T.</author>
    <title>On finite-dimensional perturbations of self-adjoint operators</title>
    <journal>J. Math. Soc. Japan</journal>
    <vol>9</vol>
    <year>1957</year>
    <page>239-249</page>
    <mr>MR0092132</mr>
  </article>

  <article>
    <bibitem>Ka 2</bibitem>
    <author>Kato, T.</author>
    <title>Perturbation of continuous spectra by trace class operators</title>
    <journal>Proc. Japan Acad.</journal>
    <vol>33</vol>
    <year>1957</year>
    <page>260-264</page>
    <mr>MR0092133</mr>
    <score>100</score>
    <query_string>Cache/Ka/Kato,Perturbation,Proc*,1957,1958</query_string>
  </article>

  <book>
    <bibitem>Ka 3</bibitem>
    <author>Kato, T.</author>
    <booktitle>Perturbation Theory for Linear Operators</booktitle>
    <publisher>Springer-Verlag, Berlin Heidelberg New York</publisher>
    <year>1966</year>
    <mr>MR0203473</mr>
    <score>100</score>
    <query_string>Cache/Ka/Kato,Perturbation,*,1966,1967</query_string>
    <page>xix+592</page>
  </book>

  <article>
    <bibitem>Ku 1</bibitem>
    <author>Kuroda, S. T.</author>
    <title>On the existence and the unitary property of the scattering operator</title>
    <journal>Nuovo Cimento</journal>
    <vol>12</vol>
    <year>1959</year>
    <page>431-454</page>
    <score>80</score>
    <query_string>Cache/Ku/Kuroda,scattering,Nuovo*,1959,1960</query_string>
  </article>

  <article>
    <bibitem>Ku 2</bibitem>
    <author>Kuroda, S. T.</author>
    <title>Scattering theory for differential operators, I, operator theory</title>
    <journal>J. Math. Soc. Japan</journal>
    <vol>25</vol>
    <year>1973</year>
    <page>75-104</page>
    <mr>MR0326435</mr>
    <query_string>Cache/Ku/Kuroda,diffferential,J*,1973,1974</query_string>
  </article>

  <book>
    <bibitem>L-P</bibitem>
    <author>Lax, P. D.; Phillips, R. S.</author>
    <booktitle>Scattering Theory</booktitle>
    <publisher>Academic Press, New York</publisher>
    <year>1967</year>
    <mr>MR0217440</mr>
    <score>100</score>
    <query_string>Cache/La/Lax,Scattering,*,1967,1968</query_string>
    <page>xii+276 pp. (1 plate)</page>
  </book>

  <article>
    <bibitem>Ly 1</bibitem>
    <author>Lyford, W. C.</author>
    <title>A two Hilbert space scattering theorem</title>
    <journal>Math. Ann.</journal>
    <vol>217</vol>
    <year>1975</year>
    <page>257-261</page>
    <mr>MR0448127</mr>
    <score>100</score>
    <query_string>Cache/Ly/Lyford,scattering,Math*,1975,1976</query_string>
  </article>

  <article>
    <bibitem>Ly 2</bibitem>
    <author>Lyford, W. C.</author>
    <title>Spectral analysis of the Laplacian in domains with cylinders</title>
    <journal>Math. Ann.</journal>
    <vol>218</vol>
    <year>1975</year>
    <page>229-251</page>
    <mr>MR0387833</mr>
    <score>100</score>
    <query_string>Cache/Ly/Lyford,Laplacian,Math*,1975,1976</query_string>
  </article>

  <article>
    <bibitem>Sh 1</bibitem>
    <author>Shimizu, S.</author>
    <title>Eigenfunction expansions for elastic wave propagation problems in stratified media $R^3$</title>
    <journal>Tsukuba J. Math.</journal>
    <vol>18</vol>
    <year>1994</year>
    <page>283-350</page>
    <mr>MR1305818</mr>
    <score>84</score>
    <query_string>Cache/Sh/Shimizu,Eigenfunction,Tsukuba*,1994,1995</query_string>
  </article>

  <article>
    <bibitem>Sh 2</bibitem>
    <author>Shimizu, S.</author>
    <title>Energy distribution of the solutions of elastic wave propagation problems in stratified media $R^3$</title>
    <journal>Tsukuba J. Math.</journal>
    <vol>19</vol>
    <year>1995</year>
    <page>409-444</page>
    <mr>MR1366645</mr>
    <score>87</score>
    <query_string>Cache/Sh/Shimizu,distribution,Tsukuba*,1995,1996</query_string>
  </article>

  <article>
    <bibitem>Sh 3</bibitem>
    <author>Shimizu, S.</author>
    <title>The limiting absorption principle for elastic wave propagation problems in perturbed stratified media $R^3$</title>
    <journal>Math. Meth. in the Appl. Sci.</journal>
    <year>1995</year>
    <page>187-215</page>
    <mr>MR1371774</mr>
    <score>87</score>
    <query_string>Cache/Sh/Shimizu,propagation,Math*,1995,1996</query_string>
  </article>

  <article>
    <bibitem>S-S</bibitem>
    <author>Shibata, Y.; Soga, H.</author>
    <title>Scattering theory for the elastic wave equation</title>
    <journal>Publ. RIMS, Kyoto Univ.</journal>
    <vol>25</vol>
    <year>1989</year>
    <page>861-887</page>
    <mr>MR1045996</mr>
    <score>100</score>
    <query_string>Cache/Sh/Shibata,Scattering,Publ*,1989,1990</query_string>
  </article>

  <article>
    <bibitem>Se</bibitem>
    <author>Stinespring, W. F.</author>
    <title>A sufficient condition for an integral operator to have a trace</title>
    <journal>J. Reine Angew. Math.</journal>
    <vol>200</vol>
    <year>1958</year>
    <page>200-207</page>
    <mr>MR0098986</mr>
    <query_string>Cache/St/Steinespring,sufficient,J*,1958,1959</query_string>
  </article>

  <book>
    <bibitem>So</bibitem>
    <author>Stone, M. H.</author>
    <booktitle>Linear Transformations in Hilbert Space and Their Applications to Analysis</booktitle>
   <publisher>vol. XV, Amer. Math. Soc. Colloquium Publ.</publisher>
    <year>1932</year>
    <mr>MR1550259</mr>
    <query_string>Cache/St/Stone,Transformations,*,1932,1933</query_string>
  </book>

  <article>
    <bibitem>S-W</bibitem>
    <author>Schulenberger, J. R.; Wilcox, C. H.</author>
    <title>Completeness of the wave operators for perturbations of uniformly propagative systems</title>
    <journal>J. Funct. Anal.</journal>
    <vol>7</vol>
    <year>1971</year>
    <page>447-474</page>
    <mr>MR0275221</mr>
    <score>100</score>
    <query_string>Cache/Sc/Schulenberger,perturbations,J*,1971,1972</query_string>
  </article>

  <article>
    <bibitem>We 1</bibitem>
    <author>Weder, R.</author>
    <title>Analyticity of the scattering matrix for wave propagation in crystals</title>
    <journal>J. Math, pures et appl.</journal>
    <vol>64</vol>
    <year>1985</year>
    <page>121-148</page>
    <mr>MR0820115</mr>
    <score>100</score>
    <query_string>Cache/We/Weder,Analyticity,J*,1985,1986</query_string>
  </article>

  <article>
    <bibitem>We 2</bibitem>
    <author>Weder, R.</author>
    <title>Spectral and scattering theory in perturbed stratified fluids</title>
    <journal>J. Math. pures et appl.</journal>
    <vol>64</vol>
    <year>1985</year>
    <page>149-173</page>
    <mr>MR0820116</mr>
    <score>100</score>
    <query_string>Cache/We/Weder,scattering,J*,1985,1986</query_string>
  </article>

  <article>
    <bibitem>Wi 1</bibitem>
    <author>Wilcox, C. H.</author>
    <title>Wave operators and asymptotic solutions of wave propagation problems of classical physics</title>
    <journal>Arch. Rational Mech. Anal.</journal>
    <vol>22</vol>
    <year>1966</year>
    <page>37-78</page>
    <mr>MR0199531</mr>
    <score>100</score>
    <query_string>Cache/Wi/Wilcox,propagation,Arch*,1966,1967</query_string>
  </article>

  <book>
    <bibitem>Wi 2</bibitem>
    <author>Wilcox, C. H.</author>
    <booktitle>Scattering Theory for the d'Alembert Equation in Exterior Domains</booktitle>
    <ser>Springer Lecture Notes in Mathematics</ser>
    <vol>442</vol>
    <publisher>Springer Lecture Notes in Mathematics, vol.442, Springer-Verlag, Berlin Heidelberg New York</publisher>
    <year>1975</year>
    <mr>MR0460927</mr>
    <score>100</score>
    <query_string>Cache/Wi/Wilcox,Scattering,*,1975,1976</query_string>
    <page>iii+184</page>
  </book>

</references>
</top_article>
