Isometric classification of Sobolev spaces on graphs
نویسنده
چکیده
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 G and each p which is not an even integer, there exists n ∈ N and a subspace L ⊂ `p whose group of isometries coincides with the direct product G ×Z2. 2000 Mathematics Subject Classification: 52A21, 46B03, 05C35
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