Fourier integral operators in Gevrey class on \({\mathbb{R}}^ n\) and the fundamental solution for a hyperbolic operator

DOI10.2977/prims/1195181409zbMath0574.35082OpenAlexW2090842433MaRDI QIDQ1063800

Kazuo Taniguchi

Publication date: 1984

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195181409

zbMATH Keywords

Cauchy problemparametrixGevrey classesFourier integral operatorsGevrey wave front setconstant multiplicity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Fundamental solutions to PDEs (35A08) Geometric theory, characteristics, transformations in context of PDEs (35A30) Initial value problems for PDEs with pseudodifferential operators (35S10)

Related Items (14)

A fundamental solution for a degenerate hyperbolic operator of second order and fourier integral operators of complex phase ⋮ Pseudo differential operators with multiple characteristics and gevrey singularities ⋮ Propagation of analytic and Gevrey regularity for a class of semi-linear weakly hyperbolic equations ⋮ Fourier integral operators and inhomogeneous Gevrey classes ⋮ Analytic-gevrey hypollipticity for a class of pswudo-differential operators with multiple characteristics ⋮ On instability mechanisms for inverse problems ⋮ Hölder continuity in time for SG hyperbolic systems ⋮ Fourier integral operators of infinite order on \({\mathcal D}_{L^2}^{\{\sigma\}}({\mathcal D}_{L^2}^{\{\sigma\}'})\) with an application to a certain Cauchy problem ⋮ Wave front set at infinity for tempered ultradistributions and hyperbolic equations ⋮ On the Cauchy problem for some non-Kowalewskian equations in \(\mathcal{D}^{[\sigma}_{L^ 2}\)] ⋮ Unnamed Item ⋮ Propagation of wave front sets of solutions of the Cauchy problem for a hyperbolic system in Gevrey classes ⋮ Pseudo-differential operators of infinite order on \({\mathcal D}_{L^2}^{\{\sigma\}}({\mathcal D}_{L^2}^{\{\sigma\}'})\) and applications to the Cauchy problem for some elementary operators ⋮ On multi-products of pseudo-differential operators in Gevrey classes and its application to Gevrey hypoellipticity

Cites Work

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• Singularities of solutions of the hyperbolic Cauchy problem in Gevrey classes
• Multi-products of Fourier integral operators and the fundamental solution for a hyperbolic system with involutive characteristics
• Leray-Volevich's system and Gevrey class
• Fundamental solutions for operators of regularly hyperbolic type
• Conditions for correctness in Gevrey classes of the Cauchy problem for weakly hyperbolic equations
• Irregularity of characteristic elements and hyperbolicity
• Fundamental solution of Cauchy problem for hyperbolic systems and Gevrey class
• Le problème de Cauchy pour les équations hyperboliques à caractéristique multiple
• Pseudo-differential operators and Gevrey classes
• Fundamental solution for a hyperbolic system with diagonal principal part
• Fundamental solution for a hyperbolic equation with involutive characteristics of variable multiplicity
• Multi—products ofphase functions for fourier integral opertaors with an application
• Uniqueness theorems and wave front sets for solutions of linear differential equations with analytic coefficients

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