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- W3091198450 abstract "In this paper, we will define $a$-deformed Laguerre operators $L_{a,alpha}$ and $a$-deformed Laguerre holomorphic semigroups on $L^2left(left(0,inftyright),dmu_{a,alpha}right)$. Then we give a spherical harmonic expansion, which reduces to the Bochner-type identity when taking the boundary value $z=frac{pi i}2$, of the $(k,a)$-generalized Laguerre semigroup introduced by S. Ben Said, T. Kobayashi and B. O rsted. And then we prove a Hardy inequality for fractional powers of the $a$-deformed Dunkl harmonic oscillator $triangle_{k,a}:=left|xright|^{2-a}triangle_k-left|xright|^a$ using this expansion. When $a=2$, the fractional Hardy inequality reduces to that of Dunkl--Hermite operators given by 'O. Ciaurri, L. Roncal and S. Thangavelu. The operators $L_{a,alpha}$ also give a tangible characterization of the radial part of the $(k,a)$-generalized Laguerre semigroup on each $k$-spherical component $mathcal H_k^mleft(mathbb{R}^Nright)$ for $lambda_{k,a,m}:=frac{2m+2leftlangle krightrangle+N-2}ageq -1/2$ defined via decomposition of unitary representation." @default.
- W3091198450 created "2020-10-08" @default.
- W3091198450 creator A5051871775 @default.
- W3091198450 date "2020-08-03" @default.
- W3091198450 modified "2023-09-24" @default.
- W3091198450 title "Hardy inequalities for fractional $(k,a)$-generalized harmonic oscillator" @default.
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- W3091198450 doi "https://doi.org/10.48550/arxiv.2008.00804" @default.
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