are the operators of squared mass, $M^{2}=-P^{2}$, and spin, $S=PJ/M$. In particular, choosing a representation of the discrete series $D^{\pm}_{\alpha}$ and parameter $s=\varepsilon\alpha$, $\varepsilon=\pm 1$, we find that these equations have nontrivial solutions describing the states with spin $s=\varepsilon\alpha$, mass $M=m$ and energy sign $\epsilon^0=\pm\varepsilon$. In this case eq. (\[maj\]) itself is the (2+1)-dimensional analog of the Majorana equation [@maj] giving the spectrum of the quantized model of relativistic particle with torsion [@tors]. The spectrum of this equation contains an infinite number of massive states with spin-mass dependence $$M_{n}=m\frac{\alpha}{|S_{n}|},\quad
S_{n}=\epsilon (\alpha+n),
\label{majsp}$$ and, moreover, comprises massless and tachyonic states. Therefore, from the point of view of the Majorana equation spectrum, the role of the Klein-Gordon equation consists in singling out only one state corresponding to $n=0$ from infinite spectrum (\[majsp\]) and in getting rid off the massless and tachyonic states.

The system of equations (\[kle\]) and (\[maj\]) has an essential shortcoming: they are completely independent, unlike, e.g., the systems of Dirac and Klein-Gordon equations for the case of spinor field or of Jackiw-Templeton-Schonfeld and Klein-Gordon equations for a topologically massive vector U(1) gauge field [@jts]. Therefore, they are not very suitable for constructing the action and quantum theory of the 