Relativistic oscillator: Linearly rising trajectories and structure functions

A new class of realizations of the dynamical group O(4,2) depending on an arbitrary function G is found. As a special case it is applied to a moving relativistic composite object which in its rest frame is a three-dimensional oscillator. The wave equation is exactly solved; the generators of the Poincare group are identified. It can be applied to a moving ''bag'' or bound state where the constituents are bound by a confining potential. The form factors and structure functions are discussed.