The growth of entire solutions of differential equations of finite and infinite order
Annales de l'Institut Fourier, Tome 22 (1972) no. 1, pp. 211-238.

Pour certains espaces de Fréchet de fonctions entières de plusieurs variables qui satisfont à des conditions de croissance spécifiées, nous définissons un opérateur différentiel à coefficients constants αˇ comme la transposée d’une opération de convolution dans l’espace dual de fonctionnelles linéaires continues et nous montrons que pour f(z) dans un de ces espaces, il existe toujours une solution de l’équation différentielle αˇ(x)=f dans le même espace.

For certain Fréchet spaces of entire functions of several variables satisfying some specified growth conditions, we define a constant coefficient differential operator αˇ as the transpose of a convolution operation in the dual space of continuous linear functionals and show that for f(z) in one of these spaces, their always exists a solution of the differential equation αˇ(x)=f in the same space.

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     title = {The growth of entire solutions of differential equations of finite and infinite order},
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Gruman, Lawrence. The growth of entire solutions of differential equations of finite and infinite order. Annales de l'Institut Fourier, Tome 22 (1972) no. 1, pp. 211-238. doi : 10.5802/aif.404. http://www.numdam.org/articles/10.5802/aif.404/

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