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 = {Institut Fourier}, address = {Grenoble}, volume = {37}, number = {2}, year = {1987}, doi = {10.5802/aif.1094}, mrnumber = {89d:58120}, zbl = {0607.58041}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1094/} }
TY - JOUR AU - Tose, Nobuyuki TI - 2nd microlocalisation and conical refraction JO - Annales de l'Institut Fourier PY - 1987 SP - 239 EP - 259 VL - 37 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1094/ DO - 10.5802/aif.1094 LA - en ID - AIF_1987__37_2_239_0 ER -
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. http://www.numdam.org/articles/10.5802/aif.1094/
[1] Methods of Mathematical Physics, vol. II, Interscience, 1962. | Zbl
, ,[2] Théorèmes d'annulation et deuxième microlocalisation, Prepublications d'Orsay, Univ. Paris-Sud, 1983.
, ,[3] Systems of differential equations with regular singularities and their boundary value problems, Ann. of Math., 106 (1977), 145-200. | MR | Zbl
, ,[4] 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
,[5] Thesis presented to Univ. Liège, 1983.
,[6] 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 | Zbl
,[7] Conical refraction in crystal optics and hydromagnetics, Comm. in Pure and Appl. Math., 14 (1961), 113-124. | MR | Zbl
,[8] Microlocal structure of involutive conical refraction, Duke Math. J., 46 (1979), 571-582. | MR | Zbl
, ,[9] Microfunctions and Pseudodifferential Equations, Lecture Note in Math., No 287, Springer, (1973), 265-529. | MR | Zbl
, , ,[10] Microdifferential systems in the complex domain, Grundlehren der Math., Springer, (1985). | MR | Zbl
,[11] 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 | Zbl
,[12] 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 | Zbl
,[13] On a class of 2-microhyperbolic systems I and II, preprints. | Zbl
,[14] Microlocal Study of Sheaves, Astérisque, 128 (1985). | Numdam | Zbl
, ,Cited by Sources: