Geodesic
On the Continuous Linear Right Inverse for Convolution Operators in Spaces of Ultradifferentiable Functions
Matematičeskie zametki, Tome 96 (2014) no. 4, pp. 548-566

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A surjective convolution operator is considered in spaces of complex-valued Beurling ultradifferentiable functions of normal type on a finite interval. A complete description of characteristic functions for which this operator has a continuous linear right inverse is obtained. The finite- and infinite-order differential operators with constant coefficients are studied as a special case.
Keywords: convolution operator, continuous linear right inverse (CLRI), Beurling ultradifferentiable function. 
@article{MZM_2014_96_4_a6,
     author = {D. A. Polyakova},
     title = {On the {Continuous} {Linear} {Right} {Inverse} for {Convolution} {Operators} in {Spaces} of {Ultradifferentiable} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {548--566},
     publisher = {mathdoc},
     volume = {96},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a6/}
}
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D. A. Polyakova. On the Continuous Linear Right Inverse for Convolution Operators in Spaces of Ultradifferentiable Functions. Matematičeskie zametki, Tome 96 (2014) no. 4, pp. 548-566. http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a6/