We consider extremal problems for continuous functions that are nonpositive on a closed interval and can be represented as series in Gegenbauer polynomials with nonnegative coefficients. These problems arise from the Delsarte method of finding an upper bound for the kissing number in the Euclidean space. We develop a general method for solving such problems. Using this method, we reproduce results of previous authors and find a solution in the following 11 new dimensions: 147, 157, 158, 159, 160, 162, 163, 164, 165, 167, and 173. The arising extremal polynomials are of a new type.
Translated title of the contributionDelsarte method in the problem on kissing numbers in high-dimensional spaces
Original languageRussian
Pages (from-to)224-239
Number of pages16
JournalТруды института математики и механики УрО РАН
Volume18
Issue number4
Publication statusPublished - 2012

    GRNTI

  • 27.00.00 MATHEMATICS

    Level of Research Output

  • VAK List

ID: 9229244