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Transactions of the Moscow Mathematical Society
Transactions of the Moscow Mathematical Society
ISSN 1547-738X(online) ISSN 0077-1554(print)

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


Author: V. V. Vlasov
Translated by: V. E. Nazaikinskii
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva.
Journal: Trans. Moscow Math. Soc. 2012, 121-138
MSC (2010): Primary 47G20; Secondary 34K30, 47A56, 34K12
Posted: 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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Additional Information

V. V. Vlasov
Affiliation: Faculty of Mechanics and Mathematics, Moscow State University, 1 Leninskie Gory, 119991 Moscow, Russian Federation
Email: vikvvlasov@rambler.ru

DOI: http://dx.doi.org/10.1090/S0077-1554-2013-00197-1
PII: S 0077-1554(2013)00197-1
Keywords: Integro-differential equation, operator function, exponential solution
Posted: January 24, 2013
Additional Notes: Supported by RFBR grants nos. 11-01-00790 and 11-01-12115-ofi-m-2011 and by State Support of Leading Scientific Schools grant no. NSh-7322.2010.1
Article copyright: © Copyright 2013 American Mathematical Society