The remainder in asymptotic integration II
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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
- Horst Behncke, The remainder in asymptotic integration, Proc. Amer. Math. Soc. 136 (2008), no. 9, 3231–3238. MR 2407088, DOI 10.1090/S0002-9939-08-09403-3
- Horst Behncke and Christian Remling, Uniform asymptotic integration of a family of linear differential systems, Math. Nachr. 225 (2001), 5–17. MR 1827087, DOI 10.1002/1522-2616(200105)225:1<5::AID-MANA5>3.3.CO;2-B
- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1955. MR 0069338
- M. S. P. Eastham, The asymptotic solution of linear differential systems, London Mathematical Society Monographs. New Series, vol. 4, The Clarendon Press, Oxford University Press, New York, 1989. Applications of the Levinson theorem; Oxford Science Publications. MR 1006434
Additional Information
- Horst Behncke
- Affiliation: Fachbereich Mathematik/Informatik, University of Osnabruck, D-49069 Osnabruck, Germany
- Received by editor(s): July 24, 2008
- Published electronically: January 7, 2010
- Communicated by: Bryna Kra
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 1633-1638
- MSC (2000): Primary 34E10
- DOI: https://doi.org/10.1090/S0002-9939-10-09823-0
- MathSciNet review: 2587447