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• W3183179251 abstract "Motivated by a recent study of Bessel operators in connection with a refinement of Hardy's inequality involving $ 1/sin^2(x) $ on the finite interval $ (0, pi) $, we now take a closer look at the underlying Bessel-type operators with more general inverse square singularities at the interval endpoints. More precisely, we consider quadratic forms and operator realizations in $ L^2((a, b); dx) $ associated with differential expressions of the form begin{document}$ omega_{s_a} = - frac{d^2}{dx^2} + frac{s_a^2 - (1/4)}{(x-a)^2}, quad s_a in {mathbb{R}}, ; x in (a, b), $end{document} and$ begin{align*} tau_{s_a, s_b} = - frac{d^2}{dx^2} + frac{s_a^2 - (1/4)}{(x-a)^2} + frac{s_b^2 - (1/4)}{(x-b)^2} + q(x), quad x in (a, b), & s_a, s_b in [0, infty), ; q in L^{infty}((a, b); dx), ; q text{ real-valued a.e. on } (a, b) , & end{align*} $where $ (a, b) subset {mathbb{R}} $ is a bounded interval.As an explicit illustration we describe the Krein–von Neumann extension of the minimal operator corresponding to $ omega_{s_a} $ and $ tau_{s_a, s_b} $." @default.
• W3183179251 created "2021-08-02" @default.
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• W3183179251 date "2022-01-01" @default.
• W3183179251 modified "2023-09-25" @default.
• W3183179251 title "On domain properties of Bessel-type operators" @default.
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• W3183179251 doi "https://doi.org/10.3934/dcdss.2022201" @default.
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