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Book Review

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Book Information:

Author: Sigeru Mizohata
Title: On the Cauchy problem
Additional book information: Science Press, Beijing, and Academic Press, Orlando, 1985, 177 pp., $36.00 (paper). ISBN 0-12-501660-3.

References [Enhancements On Off] (What's this?)

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  • 3. A. P. Calderón and A. Zygmund, Singular integral operators and differential equations, Amer. J. Math. 79 (1957), 901-921. MR 100768
  • 4. A. Cauchy, Mémoire sur un théorème fondamental dans le calcul intégral, C. R. Acad. Sci. Paris 14 (1842), 1020.
  • 5. A. Cauchy, Mémoire sur l'emploi du calcul des limites dans l'integration des équations aux dérivées partielles, C. R. Acad. Sci. Paris 15 (1842), 44.
  • 6. A. Cauchy, Mémoire sur l'application du calcul des limites à rintegration d'un système d 'equations aux dérivées partielles, C. R. Acad. Sci. Paris 15 (1842), 85.
  • 7. A. Cauchy, Mémoire sur les systèmes d'equations aux dérivées partielles d'ordres quelconques, et sur leur réduction à des systèmes d'equations linéaires du premier ordre, C. .R. Acad. Sci. Paris 15 (1842), 131.
  • 8. Jacques Chazarain and Alain Piriou, Introduction to the theory of linear partial differential equations, Studies in Mathematics and its Applications, vol. 14, North-Holland Publishing Co., Amsterdam-New York, 1982. Translated from the French. MR 678605
  • 9. G. B. Folland, Lectures on partial differential equations, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 70, Published for the Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin, 1983. MR 696577
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  • 11. M. Gevrey, Sur les fonctions indéfinement dérivables de classe donnée et leur rôle dans la théorie des équations partielles, C. R. Acad. Sci. Paris 157 (1913), 1121-1124.
  • 12. J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations, Yale Univ. Press, New Haven, CT, 1923.
  • 13. E. Holmgren, Über Systeme von linearen partiellen Differentialgleichungen, Öfversigt af Kongl. Vetenskap-Akad. Förh. 58 (1901), 91-103.
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  • 15. L. Hörmander, Linear differential operators, Actes Congr. Int. Math. Nice 1 (1970), 121-133. MR 513000
  • 16. Lars Hörmander, The analysis of linear partial differential operators. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983. Distribution theory and Fourier analysis. MR 717035
  • 17. J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269-305. MR 176362
  • 18. S. Kowalevsky, Zur Theorie der partiellen Differentialgleichungen, J. Reine Angew. Math. 80 (1875), 1-32.
  • 19. P. D. Lax, Asymptotic solutions of oscillatory initial value problems, Duke Math. J. 24 (1957), 627-646. MR 97628
  • 20. S. G. Mihlin, On the multipliers of Fourier integrals, Dokl. Akad. Nauk SSSR 109 (1956), 701-703. (Russian) MR 80799
  • 21. S. Mizohata, Some remarks on the Cauchy problem, J. Math. Kyoto Univ. 1 (1961), 109-127. MR 170112
  • 22. I. G. Petrowsky, Über das Cauchysche Problem für Systeme von partiellen Differentialgleichungen, Mat. Sb. 2(44) (1937), 815-870.
  • 23. I. G. Petrowsky, Über das Cauchysche Problem für ein System linearer partieller Differentialgleichungen im Gebiete der nichtanalytischen Funktionen, Bull. Univ. Moscow Ser. Int. 1(7) (1938), 1-74.
  • 24. M. Sato, Regularity of hyperfunction solutions of partial differential equations, Actes Congr. Int. Math. Nice 2 (1970), 785-794. MR 650826
  • 25. Michael E. Taylor, Pseudodifferential operators, Princeton Mathematical Series, vol. 34, Princeton University Press, Princeton, N.J., 1981. MR 618463
  • 26. François Trèves, Introduction to pseudodifferential and Fourier integral operators. Vol. 2, Plenum Press, New York-London, 1980. Fourier integral operators; The University Series in Mathematics. MR 597145

Review Information:

Reviewer: Michael Beals
Journal: Bull. Amer. Math. Soc. 17 (1987), 169-176
American Mathematical Society