This article is cited in 1 paper

On the Properties of Rings of Integro-Differential Operators and Their Corresponding Equations

V. F. Chistyakov

Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk

Abstract: The paper deals with systems of linear integro-differential equations, including systems with a matrix identically degenerate in the domain at the highest derivative of the unknown vector function. A theorem on the solvability of such systems of equations is proved. On the basis of this theorem, it is shown that the ring of operators corresponding to these systems contains the semigroup of operators for which a left inverse operator from this ring is found.

Keywords: integro-differential equations, degenerate equations, index, ring.

UDC: 517.968.7

Received: 11.01.2022
Revised: 25.03.2022

DOI: 10.4213/mzm13412

 English version: Mathematical Notes, 2022, 112:2, 303–308

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