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arXiv · 2406.16389

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

Patrick Guidotti·Philippe Laurençot·Christoph Walker
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Abstract

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

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Patrick Guidotti, Philippe Laurençot, Christoph Walker. 2024-06-24. Analytic semigroups in weighted $L_1$-spaces on the half-line generated by singular or degenerate operators. https://arxiv.org/abs/2406.16389

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