Most articles contain complete proofs and excellent bibliographies. For graduate students and mathematical physicists as well as mathematicians in analysis and PDEs. 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 subriemannian geometry. Contributors: R. Beals, Y. Choquet-Bruhat, F. Colombini, M. De Gosson, B. Gaveau, D. Gourdin, P. Greiner, Y. Hamada, K. Mizohata, T. Nishitani, T. Okaji, S. Ouchi, Y. Ohya, S. Spagnolo, J. Vaillant, C. Wagschal, S. Wakabayashi The book is suitable as a reference text for graduate students and active researchers.

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.

Presenting research from more than 30 international authorities, this reference provides a complete arsenal of tools and theorems to analyze systems of hyperbolic partial differential equations. The authors investigate a wide variety of problems in areas such as thermodynamics, electromagnetics, fluid dynamics, differential geometry, and topology. Renewing thought in the field of mathematical physics, Hyperbolic Differential Operators defines the notion of pseudosymmetry for matrix symbols of order zero as well as the notion of time function. Surpassing previously published material on the topic, this text is key for researchers and mathematicians specializing in hyperbolic, SchrA

dinger, Einstein, and partial differential equations; complex analysis; and mathematical physics."