  General solutions of relativistic wave equations are studied in terms of the
functions on the Lorentz group. A close relationship between hyperspherical
functions and matrix elements of irreducible representations of the Lorentz
group is established. A generalization of the Gel'fand-Yaglom formalism for
higher-spin equations is given. It is shown that a two-dimensional complex
sphere is associated with the each point of Minkowski spacetime. The separation
of variables in a general relativistically invariant system is obtained via the
hyperspherical functions defined on the surface of the two-dimensional complex
sphere. In virtue of this, the wave functions are represented in the form of
series on the hyperspherical functions. Such a description allows to consider
all the physical fields on an equal footing. General solutions of the Dirac and
Weyl equations, and also the Maxwell equations in the Majorana-Oppenheimer
form, are given in terms of the functions on the Lorentz group.
