{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:42:55Z","timestamp":1776789775221,"version":"3.51.2"},"reference-count":13,"publisher":"American Mathematical Society (AMS)","issue":"266","license":[{"start":{"date-parts":[[2009,8,27]],"date-time":"2009-08-27T00:00:00Z","timestamp":1251331200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    A discrete Fourier analysis on the dodecahedron is studied, from which results on a tetrahedron are deduced by invariance. The results include Fourier analysis in trigonometric functions, interpolation and cubature formulas on these domains. In particular, a trigonometric Lagrange interpolation on the tetrahedron is shown to satisfy an explicit compact formula and the Lebesgue constant of the interpolation is shown to be in the order of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"left-parenthesis log n right-parenthesis cubed\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>log<\/mml:mi>\n                            <mml:mo>\n                              \u2061\n                              \n                            <\/mml:mo>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:msup>\n                              <mml:mo stretchy=\"false\">)<\/mml:mo>\n                              <mml:mn>3<\/mml:mn>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">(\\log n)^3<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0025-5718-08-02156-x","type":"journal-article","created":{"date-parts":[[2009,12,1]],"date-time":"2009-12-01T13:09:23Z","timestamp":1259672963000},"page":"999-1029","source":"Crossref","is-referenced-by-count":8,"title":["Discrete Fourier analysis on a dodecahedron and a tetrahedron"],"prefix":"10.1090","volume":"78","author":[{"given":"Huiyuan","family":"Li","sequence":"first","affiliation":[]},{"given":"Yuan","family":"Xu","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2008,8,27]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/0021-9045(83)90140-5","article-title":"Bounding the Lebesgue function for Lagrange interpolation in a simplex","volume":"38","author":"Bos, L. P.","year":"1983","journal-title":"J. Approx. Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9045","issn-type":"print"},{"key":"2","series-title":"Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-6568-7","volume-title":"Sphere packings, lattices and groups","volume":"290","author":"Conway, J. H.","year":"1999","ISBN":"https:\/\/id.crossref.org\/isbn\/0387985859","edition":"3"},{"key":"3","unstructured":"D. E. Dudgeon and R. M. Mersereau, Multidimensional Digital Signal Processing, Prentice-Hall. 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(2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"key":"7","doi-asserted-by":"crossref","unstructured":"J. R. Higgins, Sampling theory in Fourier and Signal Analysis, Foundations, Oxford Science Publications, New York, 1996.","DOI":"10.1093\/oso\/9780198596998.001.0001"},{"key":"8","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/1385-7258(74)90026-2","article-title":"Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators. III","volume":"36","author":"Koornwinder, Tom H.","year":"1974","journal-title":"Indag. Math."},{"issue":"4","key":"9","doi-asserted-by":"publisher","first-page":"1653","DOI":"10.1137\/060671851","article-title":"Discrete Fourier analysis, cubature, and interpolation on a hexagon and a triangle","volume":"46","author":"Li, Huiyuan","year":"2008","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"10","series-title":"Springer Texts in Electrical Engineering","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-9708-3","volume-title":"Introduction to Shannon sampling and interpolation theory","author":"Marks, Robert J., II","year":"1991","ISBN":"https:\/\/id.crossref.org\/isbn\/0387973915"},{"key":"11","unstructured":"J. Sun, Multivariate Fourier series over a class of non tensor-product partition domains, J. Comput. Math. 21 (2003), 53-62."},{"issue":"3","key":"12","first-page":"305","article-title":"Multivariate Fourier transform methods over simplex and super-simplex domains","volume":"24","author":"Sun, Jiachang","year":"2006","journal-title":"J. Comput. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0254-9409","issn-type":"print"},{"key":"13","volume-title":"Trigonometric series. 2nd ed. Vols. I, II","author":"Zygmund, A.","year":"1959"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2009-78-266\/S0025-5718-08-02156-X\/S0025-5718-08-02156-X.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2009-78-266\/S0025-5718-08-02156-X\/S0025-5718-08-02156-X.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:57:45Z","timestamp":1776787065000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2009-78-266\/S0025-5718-08-02156-X\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,8,27]]},"references-count":13,"journal-issue":{"issue":"266","published-print":{"date-parts":[[2009,4]]}},"alternative-id":["S0025-5718-08-02156-X"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-08-02156-x","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":[[2008,8,27]]}}}