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WKB-type approximations for second-order differential equations in -algebras

Authors:	Renato Spigler Marco Vianello

Institution:	Dipartimento di Matematica, Università di Lecce, Via Provinciale Lecce-Arnesano, P.O. Box 193, 73100, Lecce, Italy ; Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, 35131, Padova, Italy

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.

Keywords:	Linear abstract differential equations WKB (Liouville-Green) approximation $C^\ast$-algebras

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