The 17 invited research articles in this volume, all written by
leading experts in their respective fields, are dedicated to the
great French mathematician Jean Leray. A wide range of topics with
significant new results---detailed proofs---are presented in the
areas of partial differential equations, complex analysis, and
mathematical physics. Key subjects are: * Treated from the
mathematical physics viewpoint: nonlinear stability of an expanding
universe, the compressible Euler equation, spin groups and the
Leray--Maslov index, * Linked to the Cauchy problem: an
intermediate case between effective hyperbolicity and the Levi
condition, global Cauchy--Kowalewski theorem in some Gevrey
classes, the analytic continuation of the solution, necessary
conditions for hyperbolic systems, well posedness in the Gevrey
class, uniformly diagonalizable systems and reduced dimension, and
monodromy of ramified Cauchy problem. Additional articles examine
results on: * Local solvability for a system of partial
differential operators, * The hypoellipticity of second order
operators, * Differential forms and Hodge theory on analytic
spaces, * Subelliptic operators and sub- Riemannian geometry.
Contributors: V. Ancona, R. Beals, A. Bove, R. Camales, Y. Choquet-
Bruhat, F. Colombini, M. De Gosson, S. De Gosson, M. Di Flaviano,
B. Gaveau, D. Gourdin, P. Greiner, Y. Hamada, K. Kajitani, M.
Mechab, K. Mizohata, V. Moncrief, N. Nakazawa, T. Nishitani, Y.
Ohya, T. Okaji, S. Ouchi, S. Spagnolo, J. Vaillant, C. Wagschal, S.
Wakabayashi The book is suitable as a reference text for graduate
students and active researchers.
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