Some remarks on boundary operators of Bessel extensions

Daniel Spector National Chiao Tung University Jesse Goodman

Analysis of PDEs mathscidoc:1804.03005

Discrete Contin. Dyn. Syst. Ser. S, 11, (3), 2018
In this paper we study some boundary operators of a class of Bessel-type Littlewood-Paley extensions whose prototype is $$ \alignat 2 \Delta_xu(x,y)+\frac{1-2s}{y}\frac{\partial u}{\partial y}(x,y)+\frac{\partial^2u}{\partial y^2}(x,y)&=0&&\qquad\text{for}\ x\in\Bbb{R}^dd,\ y>0,\\u(x,0)&=f(x)&&\qquad\text{for}\ x\in\Bbb{R}^d. \endalignat $$ In particular, we show that with a logarithmic scaling one can capture the failure of analyticity of these extensions in the limiting cases $s=k\in\Bbb{N}$.
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@inproceedings{daniel2018some,
  title={Some remarks on boundary operators of Bessel extensions},
  author={Daniel Spector, and Jesse Goodman},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180403152630599328021},
  booktitle={Discrete Contin. Dyn. Syst. Ser. S},
  volume={11},
  number={3},
  year={2018},
}
Daniel Spector, and Jesse Goodman. Some remarks on boundary operators of Bessel extensions. 2018. Vol. 11. In Discrete Contin. Dyn. Syst. Ser. S. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180403152630599328021.
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