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

Abstract

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