On three-particle integrodifferential equations

Properties of the nonlocal operators $h$ of the system of integrodifferential equations for partial components of the three-particle wave function are explored. By means of expanding the two-variables functions sought for over the known eigen-functions of the $h$ operators the equations of the system are reduced to a system of ordinary second order differential equations for one-variable functions. It is shown that the expansion used is equivalent to the application of hyperharmonic approach to the Faddeev configuration space decomposition of the Schrödinger equation.