{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T17:40:58Z","timestamp":1773250858449,"version":"3.50.1"},"reference-count":8,"publisher":"Elsevier BV","issue":"2","license":[{"start":{"date-parts":[[2003,4,1]],"date-time":"2003-04-01T00:00:00Z","timestamp":1049155200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2003,4,1]],"date-time":"2003-04-01T00:00:00Z","timestamp":1049155200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2013,8,22]],"date-time":"2013-08-22T00:00:00Z","timestamp":1377129600000},"content-version":"vor","delay-in-days":3796,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Approximation Theory"],"published-print":{"date-parts":[[2003,4]]},"DOI":"10.1016\/s0021-9045(03)00033-9","type":"journal-article","created":{"date-parts":[[2003,4,30]],"date-time":"2003-04-30T18:31:21Z","timestamp":1051727481000},"page":"199-219","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":16,"title":["On approximation of functions from Sobolev spaces on metric graphs"],"prefix":"10.1016","volume":"121","author":[{"given":"Michael","family":"Solomyak","sequence":"first","affiliation":[]}],"member":"78","reference":[{"issue":"115","key":"10.1016\/S0021-9045(03)00033-9_BIB1","first-page":"331","article-title":"Piecewise polynomial approximations of functions of classes Wp\u03b1","volume":"73","author":"Birman","year":"1967","journal-title":"Mat. Sb. (N.S.)"},{"key":"10.1016\/S0021-9045(03)00033-9_BIB2","doi-asserted-by":"crossref","unstructured":"D.E. Edmunds, H. Triebel, Function Spaces, Entropy Numbers and Differential Operators, Cambridge Tracts in Mathematics, Vol. 120, Cambridge University Press, Cambridge, 1996.","DOI":"10.1017\/CBO9780511662201"},{"key":"10.1016\/S0021-9045(03)00033-9_BIB3","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1007\/BF01445117","article-title":"Fractals, trees and the Neumann Laplacian","volume":"296","author":"Evans","year":"1993","journal-title":"Math. Ann."},{"issue":"3","key":"10.1016\/S0021-9045(03)00033-9_BIB4","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1112\/plms\/83.2.390","article-title":"The approximation numbers of Hardy-type operators on trees","volume":"83","author":"Evans","year":"2001","journal-title":"Proc. London Math. Soc."},{"issue":"3","key":"10.1016\/S0021-9045(03)00033-9_BIB5","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1112\/S0024611500012272","article-title":"Eigenvalue estimates for the weighted Laplacian on metric trees","volume":"80","author":"Naimark","year":"2000","journal-title":"Proc. London Math. Soc."},{"key":"10.1016\/S0021-9045(03)00033-9_BIB6","series-title":"n-Widths in Approximation Theory","author":"Pinkus","year":"1985"},{"key":"10.1016\/S0021-9045(03)00033-9_BIB7","doi-asserted-by":"crossref","unstructured":"M. Solomyak, On the eigenvalue estimates for the weighted Laplacian on metric graphs, in: M.Sh. Birman, S. Hildebrandt, V.A. Solonnikov, N.N. Uraltseva (Eds.), Nonlinear Problems in Mathematical Physics and Related Topics I, In Honor of Professor O.A. Ladyzhenskaya, Kluwer Academic Publishers, Dordrecht, Plenum Press, New York, 2002, pp. 326\u2013347.","DOI":"10.1007\/978-1-4615-0777-2_20"},{"key":"10.1016\/S0021-9045(03)00033-9_BIB8","series-title":"Interpolation Theory, Function Spaces \u2013 Differential Operators","author":"Triebel","year":"1978"}],"container-title":["Journal of Approximation Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021904503000339?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021904503000339?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,9,18]],"date-time":"2025-09-18T00:14:09Z","timestamp":1758154449000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0021904503000339"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,4]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2003,4]]}},"alternative-id":["S0021904503000339"],"URL":"https:\/\/doi.org\/10.1016\/s0021-9045(03)00033-9","relation":{},"ISSN":["0021-9045"],"issn-type":[{"value":"0021-9045","type":"print"}],"subject":[],"published":{"date-parts":[[2003,4]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"On approximation of functions from Sobolev spaces on metric graphs","name":"articletitle","label":"Article Title"},{"value":"Journal of Approximation Theory","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/S0021-9045(03)00033-9","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"converted-article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2003 Elsevier Science (USA). All rights reserved.","name":"copyright","label":"Copyright"}]}}