Periodic solutions of the Hill equation
The author studies the Hill equation \[ y''(t)+Ty(t)=0 \] in a Hilbert space \(H\) with periodic conditions \(y(0)=y(w); y'(0)=y'(w).\) By transforming the above equation into a first order differential equation in the space \(H_T=D(T^{1/2})\bigoplus D(T^{1/2})\) and using the semi-group formula, he shows that it is solvable and that the solutions can be expressed in terms of the generalized Green's operator.
scientific article; zbMATH DE number 6353852