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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



General solution of the homogeneous convolution equation in spaces of ultradifferentiable functions

Author: D. A. Polyakova
Translated by: V. V. Kapustin
Original publication: Algebra i Analiz, tom 31 (2019), nomer 1.
Journal: St. Petersburg Math. J. 31 (2020), 85-105
MSC (2010): Primary 44A35; Secondary 46E10
Published electronically: December 3, 2019
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Abstract: An exponential-polynomial basis is constructed in the space of all solutions of a homogeneous convolution equation in the Beurling spaces of ultradifferentiable functions of mean type on the real axis.

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Additional Information

D. A. Polyakova
Affiliation: Southern Federal University, Mil′chakov str. 8a, 344090 Rostov-on-Don, Russia; Southern Mathematical Institute of Vladikavkaz Scientific Center of RAS, Markus str. 22, 362027 Vladikavkaz, Russia

Keywords: Ultradifferentiable functions, convolution equation, differential equation of infinite order
Received by editor(s): November 26, 2017
Published electronically: December 3, 2019
Article copyright: © Copyright 2019 American Mathematical Society