2nd microlocalisation and conical refraction
Annales de l'Institut Fourier, Volume 37 (1987) no. 2, pp. 239-259.

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.

Nous étudions la propagation des singularités analytiques pour les équations microdifférentielles avec réfraction conique étudiées par R. Melrose et G. Uhlmann. Nous transformons les équations en une forme canonique simple 2-microlocalement par des transformations bicanoniques quantifiées par Y. Laurent.

@article{AIF_1987__37_2_239_0,
     author = {Tose, Nobuyuki},
     title = {2nd microlocalisation and conical refraction},
     journal = {Annales de l'Institut Fourier},
     pages = {239--259},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {37},
     number = {2},
     year = {1987},
     doi = {10.5802/aif.1094},
     zbl = {0607.58041},
     mrnumber = {89d:58120},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1094/}
}
TY  - JOUR
TI  - 2nd microlocalisation and conical refraction
JO  - Annales de l'Institut Fourier
PY  - 1987
DA  - 1987///
SP  - 239
EP  - 259
VL  - 37
IS  - 2
PB  - Imprimerie Durand
PP  - 28 - Luisant
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1094/
UR  - https://zbmath.org/?q=an%3A0607.58041
UR  - https://www.ams.org/mathscinet-getitem?mr=89d:58120
UR  - https://doi.org/10.5802/aif.1094
DO  - 10.5802/aif.1094
LA  - en
ID  - AIF_1987__37_2_239_0
ER  - 
%0 Journal Article
%T 2nd microlocalisation and conical refraction
%J Annales de l'Institut Fourier
%D 1987
%P 239-259
%V 37
%N 2
%I Imprimerie Durand
%C 28 - Luisant
%U https://doi.org/10.5802/aif.1094
%R 10.5802/aif.1094
%G en
%F AIF_1987__37_2_239_0
Tose, Nobuyuki. 2nd microlocalisation and conical refraction. Annales de l'Institut Fourier, Volume 37 (1987) no. 2, pp. 239-259. doi : 10.5802/aif.1094. https://aif.centre-mersenne.org/articles/10.5802/aif.1094/

[1] R. Courant, D. Hilbert, Methods of Mathematical Physics, vol. II, Interscience, 1962. | Zbl: 0099.29504

[2] M. Kashiwara, Y. Laurent, Théorèmes d'annulation et deuxième microlocalisation, Prepublications d'Orsay, Univ. Paris-Sud, 1983.

[3] M. Kashiwara, T. Oshima, Systems of differential equations with regular singularities and their boundary value problems, Ann. of Math., 106 (1977), 145-200. | MR: 58 #2914 | Zbl: 0358.35073

[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. | Zbl: 0561.32013

[5] P. Laubin, Thesis presented to Univ. Liège, 1983.

[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.) | MR: 86g:58139 | Zbl: 0555.35088

[7] D. Ludwig, Conical refraction in crystal optics and hydromagnetics, Comm. in Pure and Appl. Math., 14 (1961), 113-124. | MR: 23 #B748 | Zbl: 0112.21202

[8] R. Melrose, G. Uhlmann, Microlocal structure of involutive conical refraction, Duke Math. J., 46 (1979), 571-582. | MR: 81b:58044 | Zbl: 0422.58026

[9] M. Sato, T. Kawai, M. Kashiwara, Microfunctions and Pseudodifferential Equations, Lecture Note in Math., No 287, Springer, (1973), 265-529. | MR: 54 #8747 | Zbl: 0277.46039

[10] P. Schapira, Microdifferential systems in the complex domain, Grundlehren der Math., Springer, (1985). | MR: 87k:58251 | Zbl: 0554.32022

[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. | MR: 87m:58158 | Zbl: 0637.35089

[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). | MR: 89d:58121 | Zbl: 0779.58036

[13] N. Tose, On a class of 2-microhyperbolic systems I and II, preprints. | Zbl: 0615.58038

[14] M. Kashiwara, P. Shapira, Microlocal Study of Sheaves, Astérisque, 128 (1985). | Zbl: 0589.32019

Cited by Sources: