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Transactions of the Moscow Mathematical Society

This journal, a translation of Trudy Moskovskogo Matematicheskogo Obshchestva, contains the results of original research in pure mathematics.

ISSN 1547-738X (online) ISSN 0077-1554 (print)

The 2024 MCQ for Transactions of the Moscow Mathematical Society is 0.79.

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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

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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Bibliographic Information
  • V. V. Vlasov
  • Affiliation: Faculty of Mechanics and Mathematics, Moscow State University, 1 Leninskie Gory, 119991 Moscow, Russian Federation
  • Email: vikvvlasov@rambler.ru
  • Published electronically: 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
  • © Copyright 2013 American Mathematical Society
  • Journal: Trans. Moscow Math. Soc. 2012, 121-138
  • MSC (2010): Primary 47G20; Secondary 34K30, 47A56, 34K12
  • DOI: https://doi.org/10.1090/S0077-1554-2013-00197-1
  • MathSciNet review: 3184970