Kunihiko Kajitani – författare

A wide range of topics in partial differential equations, complex analysis, and mathematical physics are presented to commemorate the memory of the great French mathematician Jean Leray. The 17 research articles are written by some of the world's leading mathematicians who explore important current subjects. Most articles contain complete proofs and excellent bibliographies. For graduate students and mathematical physicists as well as mathematicians in analysis and PDEs.

A wide range of topics in partial differential equations, complex analysis, and mathematical physics are presented to commemorate the memory of the great French mathematician Jean Leray. The 17 research articles are written by some of the world's leading mathematicians who explore important current subjects. Most articles contain complete proofs and excellent bibliographies. For graduate students and mathematical physicists as well as mathematicians in analysis and PDEs.

A wide range of topics in partial differential equations, complex analysis, and mathematical physics are presented to commemorate the memory of the great French mathematician Jean Leray. The 17 research articles are written by some of the world's leading mathematicians who explore important current subjects. Most articles contain complete proofs and excellent bibliographies. For graduate students and mathematical physicists as well as mathematicians in analysis and PDEs.

The approach to the Cauchy problem taken here by the authorsis based on theuse of Fourier integral operators with acomplex-valued phase function, which is a time functionchosen suitably according to the geometry of the multiplecharacteristics. The correctness of the Cauchy problem inthe Gevrey classes for operators with hyperbolic principalpart is shown in the first part. In the second part, thecorrectness of the Cauchy problem for effectively hyperbolicoperators is proved with a precise estimate of the loss ofderivatives. This method can be applied to other (non)hyperbolic problems. The text is based on a course oflectures given for graduate students but will be of interestto researchers interested in hyperbolic partial differentialequations. In the latter part the reader is expected to befamiliar with some theory of pseudo-differential operators.