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Solvability of convolution equations in the Beurling spaces of ultradifferentiable functions of mean type on an interval

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Abstract

We establish a solvability criterion for convolution equations in the Beurling classes of ultradifferentiable functions of mean type on an interval. Under study is also the question of degeneration of convolution equations into infinite-order equations with constant coefficients.

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  1. Rostov-on-Don Southern Mathematical Institute, Southern Federal University, Vladikavkaz, Russia

    D. A. Abanina

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  1. D. A. Abanina
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Correspondence to D. A. Abanina.

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Original Russian Text Copyright © 2012 Abanina D. A.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 3, pp. 477–494, May–June, 2012.

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Abanina, D.A. Solvability of convolution equations in the Beurling spaces of ultradifferentiable functions of mean type on an interval. Sib Math J 53, 377–392 (2012). https://doi.org/10.1134/S0037446612020206

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