Effectively hyperbolic Cauchy problem
speaker: Tatsuo Nishitani (Department of Mathematics, Graduate School of Science, Osaka University)abstract: Multiple characteristics Necessary conditions of Ivrii-Petkov Effective hyperbolicity Generalized flows Generalized characteristic curves Generalized bicharacteristics Microlocal hyperbolic a priori estimate, a heuristic argument Local hyperbolic a priori estimate Uniqueness results Existence theorem Deriving a priori estimate, a heuristic argument Metric with large parameters associated to a surface Symbols and weights A lemma for calculus Specializing symbols Regularization of time function $T$ Symbol $\Lambda=M\log T$ Composition formula Composition $\langle{\xi}\rangle{\gamma}{-a\rho}\#P\#\langle{\xi} \rangle{\gamma}{a\rho}$ with a parabolic $\rho$ Composition $T{-M}\#P\#TM=P{TM}$ Symbol $P{TM}$ Definition of $p(z;\zeta)$, $Q(z)$ Hyperbolicity of $p(z;\zeta)$ Estimating $\Lambda$ $Q(z)$ separates $p(z;\zeta)$ Estimating $Pj$ Estimating $P{TM}$ Estimating $Q(z)$ Estimating $S(z)=({\bar Q}\#P{TM}-\overline{ P{TM}}\#Q)2i Estimating $S(z)w$ from below Hyperbolic polynomials Semi-continuity of hyperbolic cones Applications of semi-continuity
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