Analytic semigroups in weighted $L_1$-spaces on the half-line generated by singular or degenerate operators
Volume 286 / 2026
Studia Mathematica 286 (2026), 55-90
MSC: Primary 47D06; Secondary 35J70, 35J75
DOI: 10.4064/sm250113-15-7
Published online: 24 November 2025
Abstract
Ranges of the real-valued parameters $\alpha $, $a$, $b$, and $m$ are identified for which the operator $$\mathcal A_{\alpha}(a,b)f(x):=x^\alpha \Bigl(f''(x)+\frac{a}{x}f’(x)+\frac{b}{x^2}f(x)\Bigr), \quad x \gt 0, $$ generates an analytic semigroup in $L_1((0,\infty ),x^m\mathrm dx)$.
