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WKB-type approximations for second-order differential equations in  -algebras
Author(s):
Renato
Spigler;
Marco
Vianello
Journal:
Proc. Amer. Math. Soc.
124
(1996),
1763-1771.
MSC (1991):
Primary 34E20, 34G10, 46L05
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Abstract:
Rigorous asymptotic approximations of the WKB (or Liouville-Green) type are obtained for a basis of solutions to ![$y''+[\alpha +g(t)]y=0$](/proc/1996-124-06/S0002-9939-96-03369-2/gif-abstract/img4.gif) in the framework of  -algebras. Both cases  and  are included, thus generalizing the classical theory for scalar equations developed by F.W.J. Olver to matrix as well as to infinite-dimensional equations.
References:
- 1.
- E. Hille and R.S. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc. Coll. Publ., vol. 31, Amer. Math. Soc., Providence, 1957.MR 19:664d
- 2.
- E. Hille, Lectures on ordinary differential equations, Addison-Wesley, Reading, 1969.MR 40:2939
- 3.
- F.W.J. Olver, Error bounds for the Liouville-Green (or WKB) approximation, Proc. Cambridge Philos. Soc. 57 (1961), 790-810.MR 24:A313
- 4.
- F.W.J. Olver, Asymptotics and Special Functions, Academic Press, New York, 1974. MR 55:8655
- 5.
- W. Rudin, Functional Analysis, McGraw-Hill, New York, 1973.MR 51:1315
- 6.
- D.R. Smith, Decoupling of recessive and nonrecessive solutions for a second-order system, J. Differential Equations 68 (1987), 383-399.MR 88i:34081
- 7.
- R. Spigler and M. Vianello, Finite moments perturbations of
 in Banach algebras, Proc. Amer. Math. Soc. 119 (1993), 97-103. MR 93k:34144 - 8.
- R. Spigler and M. Vianello, Extending L'Hôpital's theorem to B-modules, J. Math. Anal. Appl. 179 (1993), 638-645.MR 94j:46050a
- 9.
- M. Vianello, A generalization of L'Hôpital's rule via absolute continuity and Banach modules, Real Anal. Exchange 18 (1993), 557-567.MR 94c:26028
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Additional Information:
Renato
Spigler
Affiliation:
Dipartimento di Matematica, Università di Lecce, Via Provinciale Lecce-Arnesano, P.O. Box 193, 73100, Lecce, Italy
Email:
spigler@ingle01.unile.it
Marco
Vianello
Affiliation:
Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, 35131, Padova, Italy
Email:
marcov@euler.math.unipd.it
DOI:
10.1090/S0002-9939-96-03369-2
PII:
S 0002-9939(96)03369-2
Keywords:
Linear abstract differential equations,
WKB (Liouville-Green) approximation,
$C^\ast$-algebras
Received by editor(s):
November 16, 1994
Additional Notes:
This work has been supported, in part, by the MURST Mathematical Analysis funds (``60\%" -funds), the GNIM-CNR, and the GNFM-CNR. Hospitality by IMA at the University of Minnesota, Minneapolis, is happily acknowledged by R.S
Communicated by:
Hal L. Smith
Copyright of article:
Copyright
1996,
American Mathematical Society
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