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We study approximation by polynomials in $$H^r(\\textbf{u})$$<\/jats:tex-math>\n \n \n H<\/mml:mi>\n r<\/mml:mi>\n <\/mml:msup>\n \n (<\/mml:mo>\n u<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, the Sobolev space consisting of functions whose derivatives of consecutive orders up to r<\/jats:italic> belong to the $$L^2$$<\/jats:tex-math>\n \n L<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> space associated with $$\\textbf{u}$$<\/jats:tex-math>\n u<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. This requires the simultaneous approximation of a function f<\/jats:italic> and its consecutive derivatives up to order $$N\\leqslant r$$<\/jats:tex-math>\n \n N<\/mml:mi>\n \u2a7d<\/mml:mo>\n r<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. We explicitly construct orthogonal polynomials that achieve such simultaneous approximation and provide error estimates in terms of $$E_n(f^{(r)})$$<\/jats:tex-math>\n \n \n E<\/mml:mi>\n n<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n \n f<\/mml:mi>\n \n (<\/mml:mo>\n r<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, the error of best approximation of $$f^{(r)}$$<\/jats:tex-math>\n \n f<\/mml:mi>\n \n (<\/mml:mo>\n r<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> in $$L^{2}(\\textbf{u})$$<\/jats:tex-math>\n \n \n L<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n \n (<\/mml:mo>\n u<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s11075-023-01572-3","type":"journal-article","created":{"date-parts":[[2023,6,30]],"date-time":"2023-06-30T03:24:47Z","timestamp":1688095487000},"page":"285-318","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Approximation by polynomials in Sobolev spaces associated with classical moment functionals"],"prefix":"10.1007","volume":"95","author":[{"given":"Juan C.","family":"Garc\u00eda-Ardila","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Misael E.","family":"Marriaga","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,6,30]]},"reference":[{"key":"1572_CR1","doi-asserted-by":"publisher","first-page":"593","DOI":"10.4310\/MAA.1999.v6.n4.a10","volume":"6","author":"M Alfaro","year":"1999","unstructured":"Alfaro, M., P\u00e9rez, T.E., Pi\u00f1ar, M.A., Rezola, M.L.: Sobolev orthogonal polynomials: the discrete-continuous case. 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