Wiener-Hopf equation and Fredholm property of the Goursat problem in Gevrey space

DOI10.1017/S0027763000005018zbMath0807.45002MaRDI QIDQ4313394

Masatake Miyake, Masafumi Yoshino

Publication date: 16 November 1994

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Fredholm propertyfactorizationGoursat problemWiener-Hopf equationGevrey indexintegro-differential operatorToeplitz symbolGevrey space

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) (Semi-) Fredholm operators; index theories (47A53) Integral operators (45P05) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Integro-differential operators (47G20)

Related Items (6)

Multisummability of formal power series solutions of partial differential equations with constant coefficients ⋮ On the Borel summability of divergent solutions of the heat equation ⋮ Fredholm property of partial differential operators of irregular singular type ⋮ Recent progress in the theory of formal solutions for ODE and PDE. ⋮ Summable solutions of the Goursat problem for some partial differential equations with constant coefficients ⋮ Asymptotic existence theorems for formal power series whose coefficients satisfy certain partial differential recursions

Cites Work

• An application of generalized implicit function theorem to Goursat problems for nonlinear Leray-Volevich systems
• Spectral property of Goursat problems
• Global and local goursat problems in a class of holomorphic or partially holomorphic functions
• Newton polygons and formal Gevrey indices in the Cauchy-Goursat-Fuchs type equations
• An operator \(L=aI-D_ t^ j D_ x^{-j-\alpha}-D_ t^{-j} D_ x^{j+\alpha}\) and its nature in Gevrey functions
• Une variante de la méthode de majoration de Cauchy
• Newton polygons and formal Gevrey classes
• On the solvability of nonlinear goursat problems
• Newton polygons and gevrey indices for linear partial differential operators
• On the solvability of Goursat problems and a function of number theory

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