On approximation of functions from Sobolev spaces on metric graphs Original Research Article

Some results on the approximation of functions from the Sobolev spaces on metric graphs by step functions are obtained. In particular, we show that the approximation numbers an of the embedding operator of the Sobolev space L1,p(G) on a graph G of finite length |G| into the space Lp(G,μ), where μ is an arbitrary finite Borel measure on G, satisfy the inequalityan⩽|G|1/p′μ(G)1/pn−1, 1