Sturm representation of the Green's function of an arbitrary number of particles interacting by the oscillator law

A Sturm representation is obtained for the Green's function of an arbitrary number of particles interacting with one another in accordance with the oscillator law. Use is made of the $K$ harmonics of the method of multidimensional hyperspherical functions and the eigenfunctions of the generalized eigenvatue problem for the oscillator potential. From the obtained results, the Sturm representation for the Green's function of noninteracting particles is obtained as a special case at oscillator frequency $\omega=0$.