{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:47:37Z","timestamp":1776725257810,"version":"3.51.2"},"reference-count":10,"publisher":"American Mathematical Society (AMS)","issue":"234","license":[{"start":{"date-parts":[[2001,2,23]],"date-time":"2001-02-23T00:00:00Z","timestamp":982886400000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    The purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula that uses\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"m\">\n                        <mml:semantics>\n                          <mml:mi>m<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">m<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    values of linear functionals (integrals over hyperspheres) and is exact for all\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"2 m\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                            <mml:mi>m<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">2m<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -harmonic functions, and consequently, for all algebraic polynomials of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n\">\n                        <mml:semantics>\n                          <mml:mi>n<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    variables of degree\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"4 m minus 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>4<\/mml:mn>\n                            <mml:mi>m<\/mml:mi>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">4m-1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0025-5718-00-01206-0","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:17:46Z","timestamp":1027707466000},"page":"671-683","source":"Crossref","is-referenced-by-count":10,"title":["Gaussian extended cubature formulae for polyharmonic functions"],"prefix":"10.1090","volume":"70","author":[{"given":"Borislav","family":"Bojanov","sequence":"first","affiliation":[]},{"given":"Dimitar","family":"Dimitrov","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2000,2,23]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1515\/crll.1996.478.1","article-title":"Characterization of best harmonic and superharmonic \ud835\udc3f\u00b9-approximants","volume":"478","author":"Armitage, David H.","year":"1996","journal-title":"J. Reine Angew. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0075-4102","issn-type":"print"},{"key":"2","series-title":"Oxford Mathematical Monographs","isbn-type":"print","volume-title":"Polyharmonic functions","author":"Aronszajn, Nachman","year":"1983","ISBN":"https:\/\/id.crossref.org\/isbn\/0198539061"},{"issue":"215","key":"3","doi-asserted-by":"publisher","first-page":"1269","DOI":"10.1090\/S0025-5718-96-00747-8","article-title":"Integration of polyharmonic functions","volume":"65","author":"Dimitrov, Dimitar K.","year":"1996","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"4","series-title":"NATO Advanced Science Institutes Series C: Mathematical and Physical Sciences","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-2436-2","volume-title":"Approximation by solutions of partial differential equations","volume":"365","year":"1992","ISBN":"https:\/\/id.crossref.org\/isbn\/0792317009"},{"key":"5","first-page":"1","article-title":"Sull\u2019esistenza e unicit\u00e0 delle formule di quadratura gaussiane","volume":"8","author":"Ghizzetti, Aldo","year":"1975","journal-title":"Rend. Mat. (6)","ISSN":"https:\/\/id.crossref.org\/issn\/0034-4427","issn-type":"print"},{"key":"6","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/BF03341969","article-title":"Representation and uniqueness theorems for polyharmonic functions","volume":"60","author":"Hayman, W. K.","year":"1993","journal-title":"J. Anal. 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(2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2001-70-234\/S0025-5718-00-01206-0\/S0025-5718-00-01206-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2001-70-234\/S0025-5718-00-01206-0\/S0025-5718-00-01206-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:35:14Z","timestamp":1776724514000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2001-70-234\/S0025-5718-00-01206-0\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,2,23]]},"references-count":10,"journal-issue":{"issue":"234","published-print":{"date-parts":[[2001,4]]}},"alternative-id":["S0025-5718-00-01206-0"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-00-01206-0","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2000,2,23]]}}}