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The remainder in asymptotic integration II


Author: Horst Behncke
Journal: Proc. Amer. Math. Soc. 138 (2010), 1633-1638
MSC (2000): Primary 34E10
DOI: https://doi.org/10.1090/S0002-9939-10-09823-0
Published electronically: January 7, 2010
MathSciNet review: 2587447
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Abstract: Levinson's Theorem in asymptotic integration of linear differential systems is strengthened in a quantitative way. It is shown that any decay in excess of absolute integrability appears with the remainder.


References [Enhancements On Off] (What's this?)

  • 1. H. Behncke, The Remainder in Asymptotic Integration, Proc. Amer. Math. Soc. 136 (2008), no. 9, 3231-3238. MR 2407088 (2009c:34117)
  • 2. H. Behncke, C. Remling, Uniform Asymptotic Integration of a Family of Linear Differential Systems, Math. Nachr. 225 (2001), 5-17. MR 1827087 (2002d:34089)
  • 3. E. A. Coddington, N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955. MR 0069338 (16:1022b)
  • 4. M.S.P. Eastham, The Asymptotic Solution of Linear Differential Systems, London Math. Society Monographs, New Series, Vol. 4, Oxford University Press, New York, 1989. MR 1006434 (91d:34001)

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Additional Information

Horst Behncke
Affiliation: Fachbereich Mathematik/Informatik, University of Osnabruck, D-49069 Osnabruck, Germany

DOI: https://doi.org/10.1090/S0002-9939-10-09823-0
Received by editor(s): July 24, 2008
Published electronically: January 7, 2010
Communicated by: Bryna Kra
Article copyright: © Copyright 2010 American Mathematical Society

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