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On global transformations of ordinary differential equations of the second order

Václav Tryhuk (2000)

Czechoslovak Mathematical Journal

The paper describes the general form of an ordinary differential equation of the second order which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form f ( t , v y , w y + u v z ) = f ( x , y , z ) u 2 v + g ( t , x , u , v , w ) v z + h ( t , x , u , v , w ) y + 2 u w z is solved on for y 0 , v 0 .

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...

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