Abstract
The $2n$-dimensional Hamiltonian system $JY' = (\lambda A + B)Y$ on an interval $(a,b)$ is considered, where both a and b are singular points. A Green’s function is derived using separated singular boundary conditions, and it is used to show that the singular boundary value problem consisting of the differential equation and boundary conditions is self-adjoint. Then a doubly singular version of Green’s formula is derived and all self-adjoint boundary value problems arising from the differential equation are characterized. Finally, the spectral measure, generalized Fourier transform of an arbitrary function and its inverse transform for the original boundary value problem with separated boundary conditions are derived.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
