Schwartz kernels on the Heisenberg group
Bollettino dell'Unione Matematica Italiana (2003)
- Volume: 6-B, Issue: 3, page 657-666
- ISSN: 0392-4041
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topVeneruso, Alessandro. "Schwartz kernels on the Heisenberg group." Bollettino dell'Unione Matematica Italiana 6-B.3 (2003): 657-666. <http://eudml.org/doc/194743>.
@article{Veneruso2003,
abstract = {Let $H_\{n\}$ be the Heisenberg group of dimension $2n+1$. Let $\mathcal\{L\}_\{1\},\ldots, \mathcal\{L\}_\{n\}$ be the partial sub-Laplacians on $H_\{n\}$ and $T$ the central element of the Lie algebra of $H_\{n\}$. We prove that the kernel of the operator $m(\mathcal\{L\}_\{1\},\ldots, \mathcal\{L\}_\{n\},-iT)$ is in the Schwartz space $S(H_\{n\})$ if $m\in S(\mathbb\{R\}^\{n+1\} )$. We prove also that the kernel of the operator $h(\mathcal\{L\}_\{1\},\ldots, \mathcal\{L\}_\{n\})$ is in $S(H_\{n\})$ if $h\in S(\mathbb\{R\}^\{n\})$ and that the kernel of the operator $g(\mathcal\{L\}, -iT)$ is in $S(H_\{n\})$ if $g\in S(\mathbb\{R\}^\{2\})$. Here $\mathcal\{L\}= \mathcal\{L\}_\{1\}+ \ldots+\mathcal\{L\}_\{n\}$ is the Kohn-Laplacian on $H_\{n\}$.},
author = {Veneruso, Alessandro},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {657-666},
publisher = {Unione Matematica Italiana},
title = {Schwartz kernels on the Heisenberg group},
url = {http://eudml.org/doc/194743},
volume = {6-B},
year = {2003},
}
TY - JOUR
AU - Veneruso, Alessandro
TI - Schwartz kernels on the Heisenberg group
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/10//
PB - Unione Matematica Italiana
VL - 6-B
IS - 3
SP - 657
EP - 666
AB - Let $H_{n}$ be the Heisenberg group of dimension $2n+1$. Let $\mathcal{L}_{1},\ldots, \mathcal{L}_{n}$ be the partial sub-Laplacians on $H_{n}$ and $T$ the central element of the Lie algebra of $H_{n}$. We prove that the kernel of the operator $m(\mathcal{L}_{1},\ldots, \mathcal{L}_{n},-iT)$ is in the Schwartz space $S(H_{n})$ if $m\in S(\mathbb{R}^{n+1} )$. We prove also that the kernel of the operator $h(\mathcal{L}_{1},\ldots, \mathcal{L}_{n})$ is in $S(H_{n})$ if $h\in S(\mathbb{R}^{n})$ and that the kernel of the operator $g(\mathcal{L}, -iT)$ is in $S(H_{n})$ if $g\in S(\mathbb{R}^{2})$. Here $\mathcal{L}= \mathcal{L}_{1}+ \ldots+\mathcal{L}_{n}$ is the Kohn-Laplacian on $H_{n}$.
LA - eng
UR - http://eudml.org/doc/194743
ER -
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