On some classes of integro-differential equations on the half-line and related operator functions

Vlasov, V.

doi:10.1090/S0077-1554-2013-00197-1

On some classes of integro-differential equations on the half-line and related operator functions
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by V. V. Vlasov
Translated by: V. E. Nazaikinskii

Trans. Moscow Math. Soc. 2012, 121-138

DOI: https://doi.org/10.1090/S0077-1554-2013-00197-1

Published electronically: January 24, 2013

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Abstract:

We study integro-differential equations with unbounded operator coefficients on the half-line. The symbols of these equations are polynomial operator pencils perturbed by operator functions holomorphic (regular) in the left half-plane.

Results concerning the Fredholm property of initial–boundary value problems for these equations on the half-line and the properties of their exponential (elementary) solutions are established.

The properties of the derived chains constructed from the root vectors of the operator functions that are the symbols of these equations are considered.

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