Solutions to the operator equation \(i\varepsilon dy/dt=A(t)y\) on intervals containing turning points
The author studies the asymptotic behavior as \(\varepsilon \rightarrow 0\) of the solution to the equation \[ i \varepsilon \frac{dy}{dt} =A(t)y , \] where \(A(t)\) is a linear closed operator defined on a dense subset of a Banach space \(X\). The solutions to the above equation are constructed as formal asymptotic expansions as \(\varepsilon \rightarrow 0\) on intervals containing parabolic or hyperbolic turning points. A recursive scheme for finding the succesive terms of these expansions are obtained.
scientific article; zbMATH DE number 1535336