A limit theorem for a branching Wiener process with a singular branching intensity of a special type

We consider a one-dimensional branching Wiener process whose branching rate is a generalized function $-|x|^{-1-\alpha}$, where $\alpha \in(0,\frac{1}{2})$. A semigroup of operators corresponding to this process is constructed and analogs of the direct and inverse Kolmogorov equations are written out. A limit theorem on convergence to an invariant distribution is proved.