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On index theorems for linear ordinary differential operators

Michèle Loday-Richaud, Geneviève Pourcin (1997)

Annales de l'institut Fourier

We introduce and study the sheaf of Deligne to describe singular points of a linear differential operator D and we develop a technique based on homological algebra to prove index theorems for D .As particular cases, we obtain index theorems for D acting in spaces of multisummable series and a new proof of the index theorem of Malgrange in the space of convergent power series and of the index theorems of Ramis in the spaces of Gevrey series.We compute the values of these indices in terms of the formal...

On strongly asymptotically developable functions and the Borel-Ritt theorem

J. Sanz, F. Galindo (1999)

Studia Mathematica

We show that the holomorphic functions on polysectors whose derivatives remain bounded on proper subpolysectors are precisely those strongly asymptotically developable in the sense of Majima. This fact allows us to solve two Borel-Ritt type interpolation problems from a functional-analytic viewpoint.

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