Hyperbolic equations and irregularity

H. Komatsu

Séminaire Équations aux dérivées partielles (Polytechnique) (1980-1981)

  • page 1-16

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Komatsu, H.. "Hyperbolic equations and irregularity." Séminaire Équations aux dérivées partielles (Polytechnique) (1980-1981): 1-16. <http://eudml.org/doc/111769>.

@article{Komatsu1980-1981,
author = {Komatsu, H.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {irregularity; ultradifferentiable function; Cauchy problem; formally hyperbolic operator of constant multiplicity},
language = {eng},
pages = {1-16},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Hyperbolic equations and irregularity},
url = {http://eudml.org/doc/111769},
year = {1980-1981},
}

TY - JOUR
AU - Komatsu, H.
TI - Hyperbolic equations and irregularity
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1980-1981
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 16
LA - eng
KW - irregularity; ultradifferentiable function; Cauchy problem; formally hyperbolic operator of constant multiplicity
UR - http://eudml.org/doc/111769
ER -

References

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  1. [1] T. Aoki: An invariant measuring the irregularity of a differential operator and a microdifferential operator, to appear. Zbl0451.35006MR673302
  2. [2] J.M. Bony et P. Schapira: Solutions hyperfonctions du problème de Cauchy, Hyperfunctions and Pseudo-Differential Equations, Lecture Notes in Math. No. 287, 1973, PP. 82-98. Zbl0258.35062MR397211
  3. [3] J. Chazarain: Opérateurs hyperboliques à caracteristiques de multiplicité constante, Ann. Inst. Fourier, Grenoble, 24 (1974) 173-202. Zbl0274.35045MR390512
  4. [4] J.C. De Paris: Problème de Cauchy oscillatoire pour un opérateur différentiel à caractéristiques multiples; lien avec l'hyperbolicité, J. Math. Pures Appl.51 (1972) 231-256. Zbl0221.35057MR306722
  5. [5] J.C. De Paris: Problème de Cauchy analytique à données singulières pour un opérateur differentiel bien décomposable, J. Math. Pure Appl.51 (1972) 465-488. Zbl0221.35058MR333468
  6. [6] J.C. De Paris et C. Wagschal: Problème de Cauchy non caractéristique à donnés Gevrey pour un opérateur analytique à caractéristiques multiples, J. Math. Pures Appl.57 (1978) 157-172. Zbl0391.35013MR505901
  7. [7] Y. Hamada: Problème analytique de Cauchy à caractéristiques multiples dont les données de Cauchy ont des singularités polaires, C. R. Acad. Sci., Paris, 276 (1973) A1681-1684. Zbl0256.35012MR326137
  8. [8] Y. Hamada, J. Leray et C. Wagschal: Systèmes d'équations aux dérivées partielles à caractéristiques multiples: Problème de Cauchy ramifié; Hyperbolicité partielle, J. Math. Pures Appl., 55 (1976) 297-352. Zbl0307.35056MR435614
  9. [9] H. Komatsu: Ultradistributions, I, Structure theorems and a characterization, J. Fac. Sci., Univ. Tokyo, Sec. IA 20 (1973) 25-105. Zbl0258.46039MR320743
  10. [10] H. Komatsu: Ultradistributions, II, The kernel theorem and ultradistributions with support in a submanifold, J. Fac. Sci., Univ. Tokyo, Sec. IA 24 (1977) 607-628. Zbl0385.46027MR477770
  11. [11] H. Komatsu: Ultradistributions, III, Vector valued ultradistributions and the theory of kernels, to appear. Zbl0507.46035MR687595
  12. [12] H. Komatsu: On the regularity of hyperfunction solutions of linear ordinary differential equations with real analytic coefficients, J. Fac. Sci., Univ. Tokyo, Sec. IA 20 (1973) 107-119. Zbl0266.34006MR328584
  13. [13] H. Komatsu: Irregularity of characteristic elements and construction of null-solutions, J. Fac. Sci., Univ. Tokyo, Sec. IA 23 (1976), 297-342. Zbl0443.35009MR417546
  14. [14] H. Komatsu: Irregularity of characteristic elements and hyperbolicity, Publ. RIMS, Kyoto Univ.12 Suppl. (1977) 233-245. Zbl0375.35044MR481562
  15. [15] H. Komatsu: An analogue of the Cauchy-Kowalevsky theorem for ultradifferentiable functions and a division theorem of ultradistributions as its dual, J. Fac. Sci., Univ. Tokyo, Sec. IA 26 (1979) 239-254. Zbl0424.46032MR550685
  16. [16] H. Komatsu: Linear hyperbolic equations with Gevrey coefficients, J. Math. Pures Appl.59 (1980) 145-185. Zbl0407.35052MR581987
  17. [17] J. Leray et Y. Ohya: Systèmes linéaires,, hyperboliques non stricts, Colloque CBRM, 1964, pp. 105-144. Zbl0135.14804MR190544
  18. [18] S. Matsuura: On non-strict hyperbolicity, Proc. Internat. Conf. on Functional Analysis and Related Topics, 1969, Univ. of Tokyo Press, Tokyo, 1970, pp. 171-176. Zbl0197.36901MR267272
  19. [19] S. Mizohata: Systèmes hyperboliques, J. Math. Soc. Japan11 (1959) 205-233. Zbl0109.06903MR123835
  20. [20] S. Mizohata: Solutions nulles et solutions non analytiques, J. Math. Kyoto Univ.1 (1962) 271-302. Zbl0106.29601MR142873
  21. [21] S. Öuchi: An integral representation of singular solutions of linear partial differential equations in the complex domain, J. Fac. Sci., Univ. Tokyo, Sec. IA 27 (1980) 37-85. Zbl0439.35019MR573333
  22. [22] M. Sato, T. Kawai and M. Kashiwara: Micro functions and pseudodifferential equations, Lecture Notes in Math. No. 287, Springer, 1973, pp. 265-529. Zbl0277.46039MR420735
  23. [23] C. Wagschal: Problème de Cauchy analytique, à données méromorphes, J. Math. Pures Appl.51 (1972) 375-397. Zbl0242.35016MR348286

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