On the Green type kernels on the half space in ${ℝ}^n$

Itô, Masayuki. "On the Green type kernels on the half space in ${\mathbb {R}}^n$." Annales de l'institut Fourier 28.2 (1978): 85-105. <http://eudml.org/doc/74362>.

@article{Itô1978,
abstract = {We characterize the Hunt convolution kernels $\chi $ on $\{\bf R\}^n$ ($n\ge 2$) whose the Green type kernels on $D = \lbrace (x_1,\ldots , x_n) \in \{\bf R\}^n$; $x_1&gt;0\rbrace $, $V_\chi :C_\{\bf K\}(D) \ni f $$(\chi * f - \chi * \bar\{\chi \})_D$, satisfy the domination principle. We write\begin\{\}\bar\{f\} (x\_1,x\_2,\ldots , x\_n) = f (-x\_1,x\_2,\ldots , x\_n)\end\{\}and $(~\cdot ~)_D$ the restriction of $(~\cdot ~)$ to $D$. This gives that the question raised by H.L. Jackson is affirmatively solved.},
author = {Itô, Masayuki},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {85-105},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the Green type kernels on the half space in $\{\mathbb \{R\}\}^n$},
url = {http://eudml.org/doc/74362},
volume = {28},
year = {1978},
}

TY - JOUR
AU - Itô, Masayuki
TI - On the Green type kernels on the half space in ${\mathbb {R}}^n$
JO - Annales de l'institut Fourier
PY - 1978
PB - Association des Annales de l'Institut Fourier
VL - 28
IS - 2
SP - 85
EP - 105
AB - We characterize the Hunt convolution kernels $\chi $ on ${\bf R}^n$ ($n\ge 2$) whose the Green type kernels on $D = \lbrace (x_1,\ldots , x_n) \in {\bf R}^n$; $x_1&gt;0\rbrace $, $V_\chi :C_{\bf K}(D) \ni f $$(\chi * f - \chi * \bar{\chi })_D$, satisfy the domination principle. We write\begin{}\bar{f} (x_1,x_2,\ldots , x_n) = f (-x_1,x_2,\ldots , x_n)\end{}and $(~\cdot ~)_D$ the restriction of $(~\cdot ~)$ to $D$. This gives that the question raised by H.L. Jackson is affirmatively solved.
LA - eng
UR - http://eudml.org/doc/74362
ER -