Analytic semigroups in weighted $L_1$-spaces on the half-line generated by singular or degenerate operators

Ranges of the real-valued parameters $\alpha$, $a$, $b$, and $m$ are identified for which the operator $${\mathcal{A}}_{\alpha }(a,b)f(x):=x^{\alpha }(f^{\mathrm{\prime }\mathrm{\prime }}(x)+\frac{a}{x}{f}^{\mathrm{\prime }}(x)+\frac{b}{x^2}f(x)),x>0,$$ generates an analytic semigroup in $L_1((0,\mathrm{\infty }),x^m\mathrm{d}x)$.