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The growth of entire solutions of differential equations of finite and infinite order

Lawrence Gruman — 1972

Annales de l'institut Fourier

For certain Fréchet spaces of entire functions of several variables satisfying some specified growth conditions, we define a constant coefficient differential operator α ˇ 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 α ˇ ( x ) = f in the same space.

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