2nd microlocalisation and conical refraction

Nobuyuki Tose

Annales de l'institut Fourier (1987)

  • Volume: 37, Issue: 2, page 239-259
  • ISSN: 0373-0956

Abstract

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We study the propagation of microlocal analytic singularities for the microdifferential equations with conical refraction studied by R. Melrose and G. Uhlmann. We transform the equations to a simple canonical form 2-microlocaly through quantized bicanonical transformations by Y. Laurent.

How to cite

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Tose, Nobuyuki. "2nd microlocalisation and conical refraction." Annales de l'institut Fourier 37.2 (1987): 239-259. <http://eudml.org/doc/74755>.

@article{Tose1987,
abstract = {We study the propagation of microlocal analytic singularities for the microdifferential equations with conical refraction studied by R. Melrose and G. Uhlmann. We transform the equations to a simple canonical form 2-microlocaly through quantized bicanonical transformations by Y. Laurent.},
author = {Tose, Nobuyuki},
journal = {Annales de l'institut Fourier},
keywords = {propagation; microlocal analytic singularities; microdifferential equations; conical refraction; bicanonical transformation},
language = {eng},
number = {2},
pages = {239-259},
publisher = {Association des Annales de l'Institut Fourier},
title = {2nd microlocalisation and conical refraction},
url = {http://eudml.org/doc/74755},
volume = {37},
year = {1987},
}

TY - JOUR
AU - Tose, Nobuyuki
TI - 2nd microlocalisation and conical refraction
JO - Annales de l'institut Fourier
PY - 1987
PB - Association des Annales de l'Institut Fourier
VL - 37
IS - 2
SP - 239
EP - 259
AB - We study the propagation of microlocal analytic singularities for the microdifferential equations with conical refraction studied by R. Melrose and G. Uhlmann. We transform the equations to a simple canonical form 2-microlocaly through quantized bicanonical transformations by Y. Laurent.
LA - eng
KW - propagation; microlocal analytic singularities; microdifferential equations; conical refraction; bicanonical transformation
UR - http://eudml.org/doc/74755
ER -

References

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  1. [1] R. COURANT, D. HILBERT, Methods of Mathematical Physics, vol. II, Interscience, 1962. Zbl0099.29504
  2. [2] M. KASHIWARA, Y. LAURENT, Théorèmes d'annulation et deuxième microlocalisation, Prepublications d'Orsay, Univ. Paris-Sud, 1983. 
  3. [3] M. KASHIWARA, T. OSHIMA, Systems of differential equations with regular singularities and their boundary value problems, Ann. of Math., 106 (1977), 145-200. Zbl0358.35073MR58 #2914
  4. [4] Y. LAURENT, Théorie de la deuxième microlocalisation : opérateurs 2-micro-différentiels, Thesis presented to Univ. Paris-Sud, Centre d'Orsay, 1982 ; published by Birkhauser as Progress in Math. No 53. Zbl0561.32013
  5. [5] P. LAUBIN, Thesis presented to Univ. Liège, 1983. 
  6. [6] P. LAUBIN, Réfraction conique et propagation des singularités analytiques, J. Math. pures et appl., 63 (1984), 149-168. (See also a note in Sem. de Vaillant, Univ. Paris VI, 1982.) Zbl0555.35088MR86g:58139
  7. [7] D. LUDWIG, Conical refraction in crystal optics and hydromagnetics, Comm. in Pure and Appl. Math., 14 (1961), 113-124. Zbl0112.21202MR23 #B748
  8. [8] R. MELROSE, G. UHLMANN, Microlocal structure of involutive conical refraction, Duke Math. J., 46 (1979), 571-582. Zbl0422.58026MR81b:58044
  9. [9] M. SATO, T. KAWAI, M. KASHIWARA, Microfunctions and Pseudodifferential Equations, Lecture Note in Math., No 287, Springer, (1973), 265-529. Zbl0277.46039MR54 #8747
  10. [10] P. SCHAPIRA, Microdifferential systems in the complex domain, Grundlehren der Math., Springer, (1985). Zbl0554.32022MR87k:58251
  11. [11] N. TOSE, On a class of microdifferential equations with involutory double characteristics, to appear in J. of Fac. Science, Univ. Tokyo, 33-3 (1986), 619-634. Zbl0637.35089MR87m:58158
  12. [12] N. TOSE, The 2-Microlocal Canonical Form for a Class of Microdifferential Equations and Propagation of Singularities, to appear in Publ. of RIMS, Kyoto Univ., 23-1 (1987). Zbl0779.58036MR89d:58121
  13. [13] N. TOSE, On a class of 2-microhyperbolic systems I and II, preprints. Zbl0615.58038
  14. [14] M. KASHIWARA, P. SHAPIRA, Microlocal Study of Sheaves, Astérisque, 128 (1985). Zbl0589.32019

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