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In particular, a trigonometric Lagrange interpolation on a triangle is shown to satisfy an explicit compact formula, which is equivalent to the polynomial interpolation on a planar region bounded by Steiner's hypocycloid. The Lebesgue constant of the interpolation is shown to be in the order of $(\\log n)^2$. Furthermore, a Gauss cubature is established on the hypocycloid.<\/jats:p>","DOI":"10.1137\/060671851","type":"journal-article","created":{"date-parts":[[2008,4,11]],"date-time":"2008-04-11T18:08:26Z","timestamp":1207937306000},"page":"1653-1681","source":"Crossref","is-referenced-by-count":52,"title":["Discrete Fourier Analysis, Cubature, and Interpolation on a Hexagon and a Triangle"],"prefix":"10.1137","volume":"46","author":[{"given":"Huiyuan","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiachang","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuan","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,4,11]]},"reference":[{"key":"R1","unstructured":"V. V. Arestov and E. E. Berdysheva,\n                      Tur\u00e1n's problem for positive definite functions with supports in a hexagon\n                      , Proc. Steklov Inst. Math. 2001, Approximation Theory. Asymptotical Expansions, Suppl. 1, pp. S20\u2013S29."},{"key":"R2","doi-asserted-by":"crossref","unstructured":"J. H. Conway and N. J. A. Sloane,\n                      Sphere Packings, Lattices and Groups\n                      , 3rd ed., Springer, New York, 1999.","DOI":"10.1007\/978-1-4757-6568-7"},{"key":"R3","unstructured":"D. E. Dudgeon and R. M. Mersereau,\n                      Multidimensional Digital Signal Processing\n                      , Prentice\u2013Hall, Englewood Cliffs, NJ, 1984."},{"key":"R4","doi-asserted-by":"crossref","unstructured":"C. F. Dunkl and Y. Xu,\n                      Orthogonal Polynomials of Several Variables\n                      , Encyclopedia Math. 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