WKB-type approximations for second-order differential equations in 
-algebras
Authors:
Renato Spigler and Marco Vianello
Journal:
Proc. Amer. Math. Soc. 124 (1996), 1763-1771
MSC (1991):
Primary 34E20, 34G10, 46L05
DOI:
https://doi.org/10.1090/S0002-9939-96-03369-2
MathSciNet review:
1327046
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Abstract | References | Similar Articles | Additional Information
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.
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in Banach algebras, Proc. Amer. Math. Soc. 119 (1993), 97-103. Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34E20, 34G10, 46L05
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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:
https://doi.org/10.1090/S0002-9939-96-03369-2
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
Article copyright:
© Copyright 1996
American Mathematical Society
