Solvability in Gevrey Classes of Some Nonlinear Fractional Functional Differential Equations

Our purpose in this paper is to prove, under some regularity conditions on the data, the solvability in a Gevrey class of bound −1 on the interval −1,1 of a class of nonlinear fractional functional differential equations.

Beyond gevrey regularity: Superposition and propagation of singularities

We propose the relaxation of Gevrey regularity condition by using sequences which depend on two parameters, and define spaces of ultradifferentiable functions which contain Gevrey classes. It is shown that such a space is closed under superposition, and therefore inverse closed as well. Furthermore, we study partial differential operators whose coefficients are less regular then Gevrey-type ultradifferentiable functions. To that aim we introduce appropriate wave front sets and prove a theorem on propagation of singularities. This extends related known results in the sense that assumptions on the regularity of the coefficients are weakened.

Comment on “On the Carleman Classes of Vectors of a Scalar Type Spectral Operator”

The results of three papers, in which the author inadvertently overlooks certain deficiencies in the descriptions of the Carleman classes of vectors, in particular the Gevrey classes, of a scalar type spectral operator in a complex Banach space established in “On the Carleman Classes of Vectors of a Scalar Type Spectral Operator,” Int. J. Math. Math. Sci. 2004 (2004), no. 60, 3219–3235, are observed to remain true due to more recent findings.

Développement en série de fonctions holomorphes des fonctions d'une classe de Gevrey sur l'intervalle [-1;1]

We characterize Gevrey functions on the unit interval [-1; 1] as sums of holomorphic functions in specific neighborhoods of [-1; 1]. As an application of our main theorem, we perform a simple proof for Dyn'kin's theorem of pseudoanalytic extension for Gevrey classes on [-1; 1].