  In Ukrain. J. Phys., 1967, V.12, N 5, p.741-746 it was shown how, for a given
(discrete) mass spectrum of elementary or hypothetical particles, it was
possible to construct a non-trivial algebra G containing a Poincare algebra P
as a subalgebra so that the mass operator, defined throughout the space where
one of the irreducible representations G is given, is self-conjugate and its
spectrum coincides with the given mass spectrum. Such an algebra was
constructed in explicit form for the nonrelativistic case, i.e., the generators
were written for the algebra. However, the problem of how to assign the algebra
G constructively and determine an explicit form of the mass operator in the
relativistic case has remained unsolved. In the present work we present a
solution of this problem, construct continuum analogs of the classical algebras
U(N) and Sp(2N), and show that the problem of including the Poincare algebra
can be formulated in the language of wave function equations.
