{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T10:42:45Z","timestamp":1758278565152},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2008,1,10]],"date-time":"2008-01-10T00:00:00Z","timestamp":1199923200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2009,1]]},"DOI":"10.1007\/s10444-007-9057-0","type":"journal-article","created":{"date-parts":[[2008,1,9]],"date-time":"2008-01-09T13:23:07Z","timestamp":1199884987000},"page":"37-59","source":"Crossref","is-referenced-by-count":7,"title":["The s-energy of spherical designs on S 2"],"prefix":"10.1007","volume":"30","author":[{"given":"Kerstin","family":"Hesse","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,1,10]]},"reference":[{"key":"9057_CR1","volume-title":"Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, volume 55 of Applied Mathematics Series","author":"M. Abramowitz","year":"1972","unstructured":"Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, volume 55 of Applied Mathematics Series. National Bureau of Standards, Gaithersburg (1972)"},{"issue":"5","key":"9057_CR2","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1080\/10652460500431859","volume":"17","author":"J.S. Brauchart","year":"2006","unstructured":"Brauchart, J.S.: About the second term of the asymptotics for optimal Riesz energy on the sphere in the potential-theoretical case. Integral Transform. Spec. Funct. 17(5), 321\u2013328 (2006)","journal-title":"Integral Transform. Spec. Funct."},{"issue":"6","key":"9057_CR3","doi-asserted-by":"crossref","first-page":"2326","DOI":"10.1137\/050626636","volume":"44","author":"X. Chen","year":"2006","unstructured":"Chen, X., Womersley, R.S.: Existence of solutions to systems of underdetermined equations and spherical designs. SIAM J. Numer. Anal. 44(6), 2326\u20132341 (2006)","journal-title":"SIAM J. Numer. Anal."},{"key":"9057_CR4","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/BF03187604","volume":"6","author":"P. Delsarte","year":"1977","unstructured":"Delsarte, P., Goethals, J.M., Seidel, J.J.: Spherical codes and designs. Geom. Dedicata. 6, 363\u2013388 (1977)","journal-title":"Geom. Dedicata."},{"key":"9057_CR5","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/s11118-006-9032-2","volume":"26","author":"P.D. Dragnev","year":"2007","unstructured":"Dragnev, P.D., Saff, E.B.: Riesz spherical potentials with external fields and minimum energy points separation. Potential Anal. 26, 139\u2013162 (2007)","journal-title":"Potential Anal."},{"key":"9057_CR6","volume-title":"Tables of Integral Transforms, volume 2 of California Institute of Technology, Bateman Manuscript Project","author":"A. Erd\u00e9lyi","year":"1954","unstructured":"Erd\u00e9lyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Tables of Integral Transforms, volume 2 of California Institute of Technology, Bateman Manuscript Project. McGraw-Hill, New York (1954)"},{"key":"9057_CR7","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1007\/BF02711518","volume":"15","author":"R.H. Hardin","year":"1996","unstructured":"Hardin, R.H., Sloane, N.J.A.: McLaren\u2019s improved snub cube and other new spherical designs in three dimensions. Discrete Comput. Geom. 15, 429\u2013441 (1996)","journal-title":"Discrete Comput. Geom."},{"key":"9057_CR8","doi-asserted-by":"crossref","unstructured":"Hesse, K., Leopardi, P.: The Coulomb energy of spherical designs on S 2. Adv. Comput. Math. (2007), doi: 10.1007\/s10444-007-9026-7","DOI":"10.1007\/s10444-007-9026-7"},{"key":"9057_CR9","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1017\/S0004972700038041","volume":"71","author":"K. Hesse","year":"2005","unstructured":"Hesse, K., Sloan, I.H.: Worst-case errors in a Sobolev space setting for cubature over the sphere S 2. Bull. Austral. Math. Soc. 71, 81\u2013105 (2005)","journal-title":"Bull. Austral. Math. Soc."},{"key":"9057_CR10","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.jat.2006.01.004","volume":"141","author":"K. Hesse","year":"2006","unstructured":"Hesse, K., Sloan, I.H.: Cubature over the sphere S 2 in Sobolev spaces of arbitrary order. J. Approx. Theory 141, 118\u2013133 (2006)","journal-title":"J. Approx. Theory"},{"issue":"2","key":"9057_CR11","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1080\/10652469308819013","volume":"1","author":"J. Korevaar","year":"1993","unstructured":"Korevaar, J., Meyers, J.L.H.: Spherical Faraday cage for the case of equal point charges and Chebyshev-type quadrature on the sphere. Integral Transform Spec. Funct. 1(2), 105\u2013117 (1993)","journal-title":"Integral Transform Spec. Funct."},{"issue":"2","key":"9057_CR12","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1090\/S0002-9947-98-02119-9","volume":"350","author":"A.B.J. Kuijlaars","year":"1998","unstructured":"Kuijlaars, A.B.J., Saff, E.B.: Asymptotics for minimal discrete energy on the sphere. Trans. Amer. Math. Soc. 350(2), 523\u2013538 (1998)","journal-title":"Trans. Amer. Math. Soc."},{"key":"9057_CR13","doi-asserted-by":"crossref","first-page":"647","DOI":"10.4310\/MRL.1994.v1.n6.a3","volume":"1","author":"E.A. Rakhmanov","year":"1994","unstructured":"Rakhmanov, E.A., Saff, E.B., Zhou, Y.M.: Minimal discrete energy on the sphere. Math. Res. Lett. 1, 647\u2013662 (1994)","journal-title":"Math. Res. Lett."},{"key":"9057_CR14","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1006\/jath.2000.3454","volume":"104","author":"M. Reimer","year":"2000","unstructured":"Reimer, M.: Hyperinterpolation on the sphere at the minimal projection order. J. Approx. Theory 104, 272\u2013286 (2000)","journal-title":"J. Approx. Theory"},{"key":"9057_CR15","volume-title":"Orthogonal Polynomials, volume 23 of American Mathematical Society Colloquium Publications","author":"G. Szeg\u00f6","year":"1975","unstructured":"Szeg\u00f6, G.: Orthogonal Polynomials, volume 23 of American Mathematical Society Colloquium Publications, 4th edn. American Mathematical Society, Providence (1975)","edition":"4"},{"issue":"2","key":"9057_CR16","doi-asserted-by":"crossref","first-page":"389","DOI":"10.2140\/pjm.1990.144.389","volume":"144","author":"G. Wagner","year":"1990","unstructured":"Wagner, G.: On means of distances on the surface of a sphere (lower bounds). Pacific. J. Math. 144(2), 389\u2013398 (1990)","journal-title":"Pacific. J. Math."},{"issue":"2","key":"9057_CR17","doi-asserted-by":"crossref","first-page":"381","DOI":"10.2140\/pjm.1992.154.381","volume":"154","author":"G. Wagner","year":"1992","unstructured":"Wagner, G.: On means of distances on the surface of a sphere. II (upper bounds). Pacific. J. Math. 154(2), 381\u2013396 (1992)","journal-title":"Pacific. J. Math."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-007-9057-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-007-9057-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-007-9057-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T17:08:10Z","timestamp":1559149690000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-007-9057-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1,10]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["9057"],"URL":"https:\/\/doi.org\/10.1007\/s10444-007-9057-0","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1,10]]}}}