Analytic semigroups in weighted $L_1$-spaces on the half-line generated by singular or degenerate operators
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910499709386752 |
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| author | Guidotti, Patrick Laurençot, Philippe Walker, Christoph |
| author_facet | Guidotti, Patrick Laurençot, Philippe Walker, Christoph |
| contents | Ranges of the real-valued parameters $α$, $a$, $b$, and $m$ are identified for which the operator $$\mathcal{A}_α(a,b)f(x):=x^α\left(f''(x)+\frac{a}{x}f'(x)+\frac{b}{x^2}f(x)\right), \quad x>0,$$ generates an analytic semigroup in $L_1((0,\infty),x^m\mathrm{d}x)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16389 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytic semigroups in weighted $L_1$-spaces on the half-line generated by singular or degenerate operators Guidotti, Patrick Laurençot, Philippe Walker, Christoph Analysis of PDEs Ranges of the real-valued parameters $α$, $a$, $b$, and $m$ are identified for which the operator $$\mathcal{A}_α(a,b)f(x):=x^α\left(f''(x)+\frac{a}{x}f'(x)+\frac{b}{x^2}f(x)\right), \quad x>0,$$ generates an analytic semigroup in $L_1((0,\infty),x^m\mathrm{d}x)$. |
| title | Analytic semigroups in weighted $L_1$-spaces on the half-line generated by singular or degenerate operators |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.16389 |