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arXiv · 2608.19516

Higher order logarithms of Bessel operators and an extension problem

Jorge J. Betancor·Estefanía. Dalmasso·Juan C. Fariña·Pablo Quijano
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Abstract

We consider the Bessel operator defined by \[ B_λ=-\frac{d^2}{dx^2}+\frac{λ^2-1/4}{x^2}, \] on $(0,\infty)$, with $λ>-1$. We study the fractional power $B_λ^s$, $s\in (-1,1)$, $s\neq 0$, and the logarithm $\log^kB_λ$, $k\in \mathbb N$, of $B_λ$. We obtain pointwise representations of these operators and asymptotic Taylor expansions of the operators $B_λ^s$ in terms of logarithmic operators $\log^kB_λ$. We also obtain $\log B_λ$ as the solution of an extension problem.

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Jorge J. Betancor, Estefanía. Dalmasso, Juan C. Fariña, Pablo Quijano. 2026-08-20. Higher order logarithms of Bessel operators and an extension problem. https://arxiv.org/abs/2608.19516

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