Isometric classification of Sobolev spaces on graphs
Colloquium Mathematicum, Tome 109 (2007) no. 2, pp. 287-295
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Isometric Sobolev spaces on finite graphs
are characterized. The characterization implies that the following
analogue of the Banach–Stone theorem is valid: if two Sobolev
spaces on $3$-connected graphs, with the exponent which is not an
even integer, are isometric, then the corresponding graphs are
isomorphic. As a corollary it is shown that for each finite group
$\mathcal{G}$ and each $p$ which is not an even integer, there exists
$n\in\mathbb{N}$ and a subspace $L\subset\ell_p^n$ whose group of
isometries is the direct product $\mathcal{G}\times\mathbb{Z}_2$.
Keywords:
isometric sobolev spaces finite graphs characterized characterization implies following analogue banach stone theorem valid sobolev spaces connected graphs exponent which even integer isometric corresponding graphs isomorphic corollary shown each finite group mathcal each which even integer there exists mathbb subspace subset ell whose group isometries direct product mathcal times mathbb
Affiliations des auteurs :
M. I. Ostrovskii 1
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author = {M. I. Ostrovskii},
title = {Isometric classification of {Sobolev} spaces on graphs},
journal = {Colloquium Mathematicum},
pages = {287--295},
publisher = {mathdoc},
volume = {109},
number = {2},
year = {2007},
doi = {10.4064/cm109-2-10},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm109-2-10/}
}
M. I. Ostrovskii. Isometric classification of Sobolev spaces on graphs. Colloquium Mathematicum, Tome 109 (2007) no. 2, pp. 287-295. doi: 10.4064/cm109-2-10
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