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Isometric classification of Sobolev spaces on graphs

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Ostrovskii M.

Colloquium Mathematicum

2007

tom 109

nr 2

287-295

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 $L ⊂ ℓⁿ_{p}$ whose group of isometries is the direct product 𝒢 × ℤ₂.

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1 Colloquium Mathematicum

1 Ostrovskii M.

1 2007

Wyniki wyszukiwania

Isometric classification of Sobolev spaces on graphs