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WKB-type approximations for second-order differential equations in $C^\ast $-algebras

Authors: Renato Spigler and Marco Vianello
Journal: Proc. Amer. Math. Soc. 124 (1996), 1763-1771
MSC (1991): Primary 34E20, 34G10, 46L05
MathSciNet review: 1327046
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Abstract: Rigorous asymptotic approximations of the WKB (or Liouville-Green) type are obtained for a basis of solutions to $y''+[\alpha +g(t)]y=0$ in the framework of $C^\ast $-algebras. Both cases $\alpha >0$ and $\alpha <0$ 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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Additional Information

Renato Spigler
Affiliation: Dipartimento di Matematica, Università di Lecce, Via Provinciale Lecce-Arnesano, P.O. Box 193, 73100, Lecce, Italy

Marco Vianello
Affiliation: Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, 35131, Padova, Italy

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