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

DOI10.1007/BF01765323zbMath0734.35164OpenAlexW2061531274MaRDI QIDQ810773

Rossella Agliardi

Publication date: 1990

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01765323

zbMATH Keywords

Cauchy problemwell-posednessGevrey classpseudodifferential operator

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Initial value problems for first-order hyperbolic systems (35L45) Initial value problems for PDEs with pseudodifferential operators (35S10) PDEs of infinite order (35R50)

Related Items (1)

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

Cites Work

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• Microhyperbolic operators in Gevrey classes
• Fourier integral operators in Gevrey class on \({\mathbb{R}}^ n\) and the fundamental solution for a hyperbolic operator
• Propagation of wave front sets of solutions of the Cauchy problem for hyperbolic equations in Gevrey classes
• Parametrix of infinite order on Gevrey spaces to the Cauchy problem for hyperbolic operators with one constant multiple characteristic
• Fundamental solution of Cauchy problem for hyperbolic systems and Gevrey class
• Fourier integral operators of infinite order on Gevrey spaces. Applications to the Cauchy problem for certain hyperbolic operators
• Opérateurs pseudodif[facuteerentiels et classes de gevrey]
• Pseudo differential operators with multiple characteristics and gevrey singularities
• Pseudodifferential operators of infinite order and Gevrey classes

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