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Factorization of solutions of convolution equations. (English) Zbl 0691.42019

The paper deals with the problem of finding necessary and sufficient conditions on distributions \(\mu_ i\), \(i=1,2\) which ensure that every \(C^{\infty}\) solution of the convolution equation \((\mu_ 1\times \mu_ 2)\times f=0\) can be written as \(f=f_ 1+f_ 2\), where \(\mu_ i\times f_ i=0\), \(i=1,2\). Also, the same problem is treated in the context of certain spaces of entire functions.
Reviewer: D.Khavinson

MSC:

42B99 Harmonic analysis in several variables
42A85 Convolution, factorization for one variable harmonic analysis
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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