Isometric classification of Sobolev spaces on graphs

M. I. Ostrovskii. "Isometric classification of Sobolev spaces on graphs." Colloquium Mathematicae 109.2 (2007): 287-295. <http://eudml.org/doc/284344>.

@article{M2007,
abstract = {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 and each p which is not an even integer, there exists n ∈ ℕ and a subspace $L ⊂ ℓⁿ_\{p\}$ whose group of isometries is the direct product × ℤ₂.},
author = {M. I. Ostrovskii},
journal = {Colloquium Mathematicae},
keywords = {Sobolev space on a graph; linear isometry; group of isometries; 3-connected graphs},
language = {eng},
number = {2},
pages = {287-295},
title = {Isometric classification of Sobolev spaces on graphs},
url = {http://eudml.org/doc/284344},
volume = {109},
year = {2007},
}

TY - JOUR
AU - M. I. Ostrovskii
TI - Isometric classification of Sobolev spaces on graphs
JO - Colloquium Mathematicae
PY - 2007
VL - 109
IS - 2
SP - 287
EP - 295
AB - 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 and each p which is not an even integer, there exists n ∈ ℕ and a subspace $L ⊂ ℓⁿ_{p}$ whose group of isometries is the direct product × ℤ₂.
LA - eng
KW - Sobolev space on a graph; linear isometry; group of isometries; 3-connected graphs
UR - http://eudml.org/doc/284344
ER -