{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T10:17:51Z","timestamp":1776766671924,"version":"3.51.2"},"reference-count":5,"publisher":"American Mathematical Society (AMS)","issue":"215","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    The results in this paper are motivated by two analogies. First,\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                    -harmonic functions in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"bold upper R Superscript n\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"bold\">R<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi>n<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbf {R}^{n}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    are extensions of the univariate algebraic polynomials of odd degree\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"2 m minus 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>2<\/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\">2m-1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Second, Gauss\u2019 and Pizzetti\u2019s mean value formulae are natural multivariate analogues of the rectangular and Taylor\u2019s quadrature formulae, respectively. This point of view suggests that some theorems concerning quadrature rules could be generalized to results about integration of polyharmonic functions. This is done for the Tchakaloff-Obrechkoff quadrature formula and for the Gaussian quadrature with two nodes.\n                  <\/p>","DOI":"10.1090\/s0025-5718-96-00747-8","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"1269-1281","source":"Crossref","is-referenced-by-count":9,"title":["Integration of polyharmonic functions"],"prefix":"10.1090","volume":"65","author":[{"given":"Dimitar","family":"Dimitrov","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"key":"1","series-title":"Oxford Mathematical Monographs","isbn-type":"print","volume-title":"Polyharmonic functions","author":"Aronszajn, Nachman","year":"1983","ISBN":"https:\/\/id.crossref.org\/isbn\/0198539061"},{"key":"2","series-title":"Mathematics and its Applications","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-8169-1","volume-title":"Spline functions and multivariate interpolations","volume":"248","author":"Bojanov, B. 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