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On solutions of convolution equations in spaces of ultradifferentiable functions


Author: D. A. Polyakova
Translated by: S. V. Kislyakov
Original publication: Algebra i Analiz, tom 26 (2014), nomer 6.
Journal: St. Petersburg Math. J. 26 (2015), 949-963
MSC (2010): Primary 44A35; Secondary 46E10
DOI: https://doi.org/10.1090/spmj/1369
Published electronically: September 21, 2015
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Abstract: A representation for a particular and the general solution is established for convolution equations in nonquasianalytic Beurling spaces ultradifferentiable functions of mean type on a finite interval. As a particular case, differential equations of infinite order with constant coefficients are studied.


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Additional Information

D. A. Polyakova
Affiliation: Southern Federal University, ul. Mil′chakova 8a, Rostov-on-Don 344090, Russia; Southern Mathematical Institute, VNTS RAS and RNO-A, ul. Markusa 22, Vladikavkaz 362027, Russia
Email: forsites1@mail.ru

DOI: https://doi.org/10.1090/spmj/1369
Keywords: Ultradifferentiable functions, convolution equations, differential equation of infinite order, series of exponentials
Received by editor(s): May 19, 2014
Published electronically: September 21, 2015
Additional Notes: Supported by RFBR (grant no. 14-01-31083)
Article copyright: © Copyright 2015 American Mathematical Society